Midshaft rating for turbomachine engines

ABSTRACT

A turbomachine engine including a high-pressure compressor, a high-pressure turbine, a combustion chamber in flow communication with the high-pressure compressor and the high-pressure turbine, and a power turbine in flow communication with the high-pressure turbine. At least one of the high-pressure compressor, the high-pressure turbine, and the power turbine comprises a ceramic matrix composite (CMC) material. The turbomachine engine includes a low-pressure shaft coupled to the power turbine and characterized by a midshaft rating (MSR) between two hundred (ft/sec)1/2 and three hundred (ft/sec)1/2. The low-pressure shaft has a redline speed between fifty and two hundred fifty feet per second (ft/sec). The turbomachine engine is configured to operate up to the redline speed without passing through a critical speed associated with a first-order bending mode of the low-pressure shaft.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part application of U.S. patentapplication Ser. No. 17/328,795, filed May 24, 2021, the entire contentsof which is incorporated by reference in its entirety.

This application is related to U.S. patent application Ser. No.17/328,800, filed May 24, 2021, U.S. patent application Ser. No.18/058,034, filed Nov. 22, 2022, and U.S. patent application Ser. No.18/058,036, filed Nov. 22, 2022. The entire contents of theaforementioned applications are incorporated by reference in theirentireties.

TECHNICAL FIELD

This application is generally directed to turbomachine engines,including turbomachine shafts, and a method of driving such turbomachineshafts in such turbomachine engines.

BACKGROUND

A turbofan engine, or turbomachinery engine, includes one or morecompressors, and a power turbine that drives a bypass fan. The bypassfan is coupled to the power turbine via a turbomachine shaft.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and advantages will be apparent fromthe following, more particular, description of various embodiments, asillustrated in the accompanying drawings, wherein like reference numbersgenerally indicate identical, functionally similar, and/or structurallysimilar elements.

FIG. 1 shows a schematic, cross-sectional view of a ducted, direct-drivegas turbine engine, taken along a centerline axis of the engine.

FIG. 2 shows a schematic, cross-sectional view of a ducted,indirect-drive gas turbine engine, taken along a centerline axis of theengine.

FIG. 3 shows a schematic view of an unducted, three-stream gas turbineengine, taken along a centerline axis of the engine.

FIG. 4 shows an enlarged view of a portion of the cross-sectional viewof FIG. 1 .

FIG. 5A shows a cross-sectional view of a steel shaft.

FIG. 5B shows a cross-sectional view of a composite shaft.

FIG. 6A shows a cross-sectional view of a uniform shaft with a constantdiameter and thickness.

FIG. 6B shows a cross-sectional view of a concave shaft with a constantdiameter and a variable thickness.

FIG. 6C shows a cross-sectional view of a convex shaft with a variablediameter and a variable thickness.

FIG. 7A shows a schematic view of a shaft using a four-bearing straddleconfiguration.

FIG. 7B shows a schematic view of a shaft using a four-bearing outboundconfiguration.

FIG. 7C shows a schematic view of a shaft using an inbound duplexconfiguration.

FIG. 7D shows a schematic view of a shaft using an outbound duplexconfiguration.

FIG. 7E shows a schematic view of a shaft using a two-bearingconfiguration.

FIG. 8A shows a schematic, cross-sectional view, taken along acenterline axis, of a ducted gas turbine engine, according to thepresent disclosure.

FIG. 8B shows a schematic, cross-sectional view, taken along acenterline axis, of a ducted gas turbine engine, according to thepresent disclosure.

FIG. 9 shows a schematic, cross-sectional view, taken along a centerlineaxis, of a ducted gas turbine engine, according to the presentdisclosure.

FIG. 10 shows a schematic, cross-sectional view, taken along acenterline axis, of ducted a gas turbine engine, according to thepresent disclosure.

FIG. 11 shows a schematic view, taken along a centerline axis, of anunducted gas turbine engine, according to the present disclosure.

FIG. 12 shows a schematic, partial cross-sectional view, taken along acenterline axis, of a gas turbine engine, according to the presentdisclosure.

FIG. 13 shows an enlarged cross-sectional view of a portion of the gasturbine engine of FIG. 12 , according to the present disclosure.

FIG. 14 shows an exemplary blade for an engine, according to the presentdisclosure.

FIG. 15 shows a table of material properties.

FIG. 16 shows a plot depicting disk bore radius change as a factor ofairfoil weight change.

FIG. 17 shows a plot depicting disk bore width change as a factor ofairfoil weight change.

FIG. 18 shows a schematic, partial cross-sectional view, taken along acenterline axis, of a gearbox for a gas turbine engine, according to thepresent disclosure.

FIG. 19A shows a first bending mode of a shaft.

FIG. 19B shows a second bending mode of a shaft.

FIG. 19C shows a third bending mode of a shaft.

FIG. 20A to 20I show a table of embodiments, according to the presentdisclosure.

FIG. 21A shows a plot depicting a range of a midshaft rating relative toa range of outer diameter redline speeds.

FIG. 21B shows a plot depicting a range of a midshaft rating relative toa range of length-diameter ratios.

FIG. 21C shows a plot depicting a range of a midshaft rating relative toa range of length-diameter ratios.

DETAILED DESCRIPTION

Additional features, advantages, and embodiments of the presentdisclosure are set forth or apparent from a consideration of thefollowing detailed description, drawings, and claims. Moreover, both theforegoing summary of the present disclosure and the following detaileddescription are exemplary and intended to provide further explanationwithout limiting the scope of the disclosure as claimed.

Various embodiments are discussed in detail below. While specificembodiments are discussed, this is done for illustration purposes only.A person skilled in the relevant art will recognize that othercomponents and configurations may be used without departing from thespirit and the scope of the present disclosure.

As used herein, the terms “first,” “second,” “third,” and “fourth” maybe used interchangeably to distinguish one component from another andare not intended to signify location or importance of the individualcomponents.

The terms “forward” and “aft” refer to relative positions within a gasturbine engine or vehicle, and refer to the normal operational attitudeof the gas turbine engine or vehicle. For example, with regard to a gasturbine engine, forward refers to a position closer to an engine inletand aft refers to a position closer to an engine nozzle or exhaust.

The terms “upstream” and “downstream” refer to the relative directionwith respect to fluid flow in a fluid pathway. For example, “upstream”refers to the direction from which the fluid flows, and “downstream”refers to the direction to which the fluid flows.

The terms “coupled,” “fixed,” “attached to,” and the like, refer to bothdirect coupling, fixing, or attaching, as well as indirect coupling,fixing, or attaching through one or more intermediate components orfeatures, unless otherwise specified herein.

The term “propulsive system” refers generally to a thrust-producingsystem, which thrust is produced by a propulsor, and the propulsorprovides the thrust using an electrically-powered motor(s), a heatengine such as a turbomachine, or a combination of electrical motor(s)and a turbomachine.

The singular forms “a”, “an”, and “the” include plural references unlessthe context clearly dictates otherwise.

As used herein, the terms “axial” and “axially” refer to directions andorientations that extend substantially parallel to a centerline of theturbine engine. Moreover, the terms “radial” and “radially” refer todirections and orientations that extend substantially perpendicular tothe centerline of the turbine engine. In addition, as used herein, theterms “circumferential” and “circumferentially” refer to directions andorientations that extend arcuately about the centerline of the turbineengine.

As used herein, “redline speed” means the maximum expected rotationalspeed of a shaft during normal operation of an engine. The redline speedmay be expressed in terms of rotations per second in Hertz (Hz),rotations per minute (RPM), or as a linear velocity of the outerdiameter of the shaft in terms of feet per second. For a gas turbineengine that has a high speed shaft and a low speed shaft, both the highspeed shaft and the low speed shaft have redline speeds.

As used herein, “critical speed” means a rotational speed of the shaftthat is about the same as the fundamental, or natural frequency of afirst-order bending mode of the shaft (e.g., the shaft rotates at eightyHz and the first-order modal frequency is eighty Hertz). When the shaftrotates at the critical speed, the shaft is expected to have a maximumamount of deflection, hence instability, due to excitation of thefirst-order bending mode of the shaft. The critical speed may beexpressed in terms of rotations per second in Hertz (Hz), rotations perminute (RPM), or as a linear velocity of the outer diameter of the shaftin terms of feet per second.

As used herein, “critical frequency” and “fundamental frequency” arereferred to interchangeably and refer to the fundamental, or naturalfrequency, of the first-order bending mode of the shaft.

The term “subcritical speed” refers to a shaft redline speed that isless than the fundamental, or natural frequency of the first-orderbending mode of the shaft (e.g., the shaft rotates at a redline speed of70 Hz while the first-order modal frequency is about 80 Hertz). When therotational speed is subcritical the shaft is more stable than whenrotating at a critical speed. A “subcritical shaft” is a shaft that hasa redline speed below the critical speed of the shaft.

The term “supercritical speed” refers to a shaft rotational speed thatis above the fundamental, or natural frequency of the first-orderbending mode of the shaft (e.g., the shaft rotates at eighty Hz whilethe first-order modal frequency is about seventy Hertz). A supercriticalshaft is less stable than a subcritical shaft because the shaft speedcan pass through the critical speed since its fundamental mode is belowthe redline speed. A “supercritical shaft” is a shaft that has a redlinespeed above the critical speed of the shaft.

The terms “low” and “high,” or their respective comparative degrees(e.g., “lower” and “higher”, where applicable), when used with thecompressor, turbine, shaft, or spool components, each refers to relativepressures and/or relative speeds within an engine unless otherwisespecified. For example, a “low-speed shaft” defines a componentconfigured to operate at a rotational speed, such as a maximum allowablerotational speed, which is lower than that of a “high-speed shaft” ofthe engine. Alternatively, unless otherwise specified, theaforementioned terms may be understood in their superlative degree. Forexample, a “low-pressure turbine” may refer to the lowest maximumpressure within a turbine section, and a “high-pressure turbine” mayrefer to the highest maximum pressure within the turbine section. Itshould further be appreciated that the terms “low” or “high” in suchaforementioned regards may additionally, or alternatively, be understoodas relative to minimum allowable speeds and/or pressures, or minimum ormaximum allowable speeds and/or pressures relative to normal, desired,steady state, etc., operation of the engine.

The term “casing” herein refers to the structure that defines an airflowpath (e.g., wall of duct, or casing). A mounting to the casing may be adirect bolted connection or through a load bearing frame.

As used herein, the term “ceramic matrix composite” (“CMC”) refers to asubgroup of composite materials and a subgroup of ceramics. The terms“CMC” and “CMC material” are used interchangeably herein. When theengine component (e.g., the higher pressure turbine module, nozzle, orblade thereof) comprises or includes “CMC” or “CMC material,” it isunderstood that the engine component may include one of, or combinationsof one or more of the ceramic matrix composite materials describedherein. Such engine component may also include non-ceramic matrixcomposite materials, such as a metal alloy (e.g., a CMC material for anairfoil and separate disk with dovetail slot made from a metal alloy).Reference to a “first” or “second” or “third” CMC material does notpreclude the materials from including multiple CMC materials, differentCMC materials, or the same CMC materials.

More specifically, CMC refers to a class of materials that includes areinforcing material (e.g., reinforcing fibers) surrounded by a ceramicmatrix phase. Generally, the reinforcing fibers provide structuralintegrity to the ceramic matrix. Some examples of matrix materials ofCMCs can include, but are not limited to, non-oxide silicon-basedmaterials (e.g., silicon carbide, silicon nitride, or mixtures thereof),oxide ceramics (e.g., silicon oxycarbides, silicon oxynitrides, aluminumoxide (Al₂O₃), silicon dioxide (SiO₂), aluminosilicates, or mixturesthereof), or mixtures thereof. Optionally, ceramic particles (e.g.,oxides of Si, Al, Zr, Y, and combinations thereof) and inorganic fillers(e.g., pyrophyllite, wollastonite, mica, talc, kyanite, andmontmorillonite) may also be included within the CMC matrix.

Some examples of reinforcing fibers of CMCs can include, but are notlimited to, non-oxide silicon-based materials (e.g., silicon carbide,silicon nitride, or mixtures thereof), non-oxide carbon-based materials(e.g., carbon), oxide ceramics (e.g., silicon oxycarbides, siliconoxynitrides, aluminum oxide (Al₂O₃), silicon dioxide (SiO₂),aluminosilicates such as mullite, or mixtures thereof), or mixturesthereof.

Generally, particular CMCs may be referred to as their combination oftype of fiber/type of matrix. For example, C/SiC forcarbon-fiber-reinforced silicon carbide; SiC/SiC for siliconcarbide-fiber-reinforced silicon carbide, SiC/SiN for silicon carbidefiber-reinforced silicon nitride; SiC/SiC—SiN for silicon carbidefiber-reinforced silicon carbide/silicon nitride matrix mixture, etc. Inother examples, the CMCs may include a matrix and reinforcing fiberscomprising oxide-based materials such as aluminum oxide (Al₂O₃), silicondioxide (SiO₂), aluminosilicates, and mixtures thereof. Aluminosilicatescan include crystalline materials such as mullite (3Al₂O₃.2SiO₂), aswell as glassy aluminosilicates.

In certain embodiments, the reinforcing fibers may be bundled and/orcoated prior to inclusion within the matrix. For example, bundles of thefibers may be formed as a reinforced tape, such as a unidirectionalreinforced tape. A plurality of the tapes may be laid up together toform a preform component. The bundles of fibers may be impregnated witha slurry composition prior to forming the preform or after formation ofthe preform. The preform may then undergo thermal processing andsubsequent chemical processing to arrive at a component formed of a CMCmaterial having a desired chemical composition. For example, the preformmay undergo a cure or burn-out to yield a high char residue in thepreform, and subsequent melt-infiltration (“MI”) with silicon, or a cureor pyrolysis to yield a silicon carbide matrix in the preform, andsubsequent chemical vapor infiltration (“CVI”) with silicon carbide.Additional steps may be taken to improve densification of the preform,either before or after chemical vapor infiltration, by injecting it witha liquid resin or polymer followed by a thermal processing step to fillthe voids with silicon carbide. CMC material as used herein may beformed using any known methods or hereinafter developed including butnot limited to melt infiltration, chemical vapor infiltration, polymerimpregnation pyrolysis (PIP) and any combination thereof.

Such materials, along with certain monolithic ceramics (i.e., ceramicmaterials without a reinforcing material), are particularly suitable forhigher temperature applications. Additionally, these ceramic materialsare lightweight compared to metal alloys (e.g., superalloys), yet canstill provide strength and durability to the component made therefrom.Therefore, such materials are currently being considered for many gasturbine components used in higher temperature sections of gas turbineengines, such as airfoils (e.g., turbines, and vanes), combustors,shrouds and other like components, that would benefit from thelighter-weight and higher temperature capability these materials canoffer. FIG. 15 compares properties of CVI type and MI type CMC materialsto metal alloys.

Here and throughout the specification and claims, range limitations arecombined, and interchanged, such ranges are identified and include allthe sub-ranges contained therein unless context or language indicatesotherwise. For example, all ranges disclosed herein are inclusive of theendpoints, and the endpoints are independently combinable with eachother.

One or more components of the turbomachine engine described herein belowmay be manufactured or formed using any suitable process, such as anadditive manufacturing process, such as a three-dimensional (3D)printing process. The use of such a process may allow such a componentto be formed integrally, as a single monolithic component, or as anysuitable number of sub-components. In particular, the additivemanufacturing process may allow such a component to be integrally formedand include a variety of features not possible when using priormanufacturing methods. For example, the additive manufacturing methodsdescribed herein enable the manufacture of shafts having uniquefeatures, configurations, thicknesses, materials, densities,passageways, headers, and mounting structures that may not have beenpossible or practical using prior manufacturing methods. Some of thesefeatures are described herein.

This disclosure and various embodiments relate to a turbomachineryengine, also referred to as a turbine engine, a gas turbine engine, aturboprop engine, or a turbomachine. These turbomachinery engines can beapplied across various technologies and industries. Various embodimentsmay be described herein in the context of aeronautical engines andaircraft machinery.

In some instances, a turbomachinery engine is configured as a directdrive engine. In other instances, a turbomachinery engine can beconfigured as an indirect drive engine with a gearbox. In someinstances, a propulsor of a turbomachinery engine can be a fan encasedwithin a fan case and/or nacelle. This type of turbomachinery engine canbe referred to as “a ducted engine.” In other instances, a propulsor ofa turbomachinery engine can be exposed (e.g., not within a fan case or anacelle). This type of turbomachinery engine can be referred to as “anopen rotor engine” or an “unducted engine.”

A turbofan engine, or turbomachinery engine, includes a core engine anda power turbine that drives a bypass fan. The bypass fan generates themajority of the thrust of the turbofan engine. The generated thrust canbe used to move a payload (e.g., an aircraft). A turbomachine shaftcoupled to the power turbine and fan (either directly or through agearbox) can experience vibrations during operation of the engine (e.g.,during rotation of the shaft). For example, when the shaft rotates atits critical speed the shaft will vibrate excessively. The excessivevibration is due primarily to excitation of a first-order beam bendingmode of the shaft. Thus, the shaft may be characterized by itsfirst-order beam bending mode, the fundamental resonance frequency(fundamental frequency) of this mode, and the shaft's critical speed ofrotation. If the first-order bending mode may be excited by a low speedshaft rate occurring during a standard operating range of the engine,undetected vibration, as well as an increased risk of whirl instability,may result.

Newer engine architectures may be characterized by faster shaft speedsfor the low-pressure turbine (LPT), and longer shafts to accommodate alonger engine core (e.g., the high-pressure compressor, the combustor,and the high-pressure turbine). Additionally, it is desirable to housethe engine core within a smaller space. These trends can result inreductions in stiffness-to-weight ratio for the shaft and structure thatinfluences dynamics of the LP shaft, which may have the effect oflowering the critical speed and/or limiting the available options forincreasing the critical speed for the LPT's shaft (referred to as thelow-speed shaft or the low-pressure (LP) shaft) so that the engineavoids operating at, or near the shaft's critical speed.

The length of the shaft, diameter of the shaft, mass of the shaft, andlocations at which the shaft is constrained (e.g., locations at whichthe shaft is supported by bearings) each affect the fundamentalfrequency of the shaft, thereby affecting the critical speeds of the LPTshaft. Changing just one of these features of the shaft can increase orlower the speed at which the shaft may rotate before experiencingvibrations at the fundamental frequency. That is, the critical speed ofthe shaft can be increased or decreased based on the aforementionedfeatures. For example, shortening the length of the shaft will increasethe stiffness of the shaft and, thus, increase the critical speed atwhich the shaft may rotate before encountering the first modevibrations. In another example, increasing the mass and/or the diameterof the shaft will similarly increase the critical speed.

The aforementioned shaft structure and features also, however, directlyaffect other components in the engine and the operation of the engineitself. For example, shortening the length of the low-pressure turbine'sshaft reduces the available space for the high-pressure compressorstages, the combustor, the low-pressure turbine stages, the low-pressurecompressor stages, ducts, mounts, and other engine components etc. This,in turn, has a negative impact on engine operation by reducing the poweroutput of the engine and reducing combustor efficiency. Indeed, there isa desire to have a lengthened high-pressure compressor or morehigh-pressure compressor stages to improve combustor efficiency.Likewise, increasing the diameter and/or mass of the low-speed shaft canhave a similar effect, reducing available space for the remaining enginecomponents and increasing weight of the engine, thus, again, negativelyimpacting engine performance. Thus, a balance is ultimately struck(penalties vs. benefits) to maintain or enhance engine performance,while also enabling an increase in the critical speed of thelow-pressure turbine shaft, or not lowering the critical speed, e.g.,add 1 or 2 additional stages to a compressor to increase efficiency, toallow for faster speeds for the power turbine while avoiding sustainedoperations at or near the critical speed. To achieve this balance,tradeoffs are made to 1) allow for a lengthened high-pressurecompressor, shortened overall length of the engine for aero-performance,or reduced nacelle length or size, or any combination thereof, while 2)shortening the low-pressure turbine shaft length, in particular, themidshaft length and increasing the shaft diameter of the low-pressureturbine shaft to increase the critical speed of the low-pressure/lowspeed turbine shaft (LP shaft).

As part of this effort, the inventors evaluated the influence of usingdifferent materials for the engine core (rotor disks, airfoils) andchanges in size of the core, and resulting impact that thesemodifications have on the dynamics of the high speed shaft, the lowspeed shaft, and the interaction between these two shafts as can occurthrough dynamic excitation transmitted through shaft bearings. It isexpected next generation engines will operate with a higher powerdensity (power/weight), which can mean lengthening the core by addingadditional compression stages to the high speed compressor.Additionally, or alternatively, a core operating at a higher powerdensity is expected to operate at higher temperatures at the compressorexit stage and the downstream turbine stages. In this regard,higher-temperature-tolerant material can be used to enable operating athigher temperatures, such as, a ceramic matrix composite (CMC) material.The use of such higher temperature-tolerant material is expected tobring about changes in weight and component size and volume, which isexpected to influence the behavior of both the high-speed shaft andmid-shaft. Thus, the inventors, as part of their investigation andevaluation of different engine architectures, also considered how thedynamics of the midshaft and high speed shaft might change when theengine core changes in size and weight, in response to a need to operateat higher power densities enabled by use of higher temperature-tolerantmaterial.

Different approaches for engine types, midshaft geometry, bearingsupport, and material compositions are needed for next-generationturbomachine engines, to permit high-speed operation without resultingin an unstable bending mode, and, therefore, vibrations during regularoperation. The inventors, tasked with finding a suitable design to meetthese requirements while lowering vibrations, or at least maintaining atolerable vibration environment during flight conditions (e.g., takeoffor max thrust), conceived and tested a wide variety of shafts havingdifferent combinations of stiffness, material, bearing type andlocation, shaft length, and diameter in order to determine whichembodiment(s) were most promising for a variety of contemplated enginedesigns, including different engine core sizes for different sizedhigh-pressure compressors and high-pressure turbines. The variousembodiments, as described herein including illustrated examples for botha ducted and open fan configuration of a gas turbine engine, includeturbomachine shafts that employ one or more of the above-mentionedtechniques to increase the critical speed of the LP shaft and/ormaintain a design speed for improved efficiency while mitigating oravoiding a subcritical or critical speed situation during flightoperations.

FIG. 1 shows a schematic, cross-sectional view of a ducted,direct-drive, gas turbine engine 100 for an aircraft, that mayincorporate one or more embodiments of the present disclosure. The gasturbine engine 100 includes a fan assembly 102 (e.g., a fixed-pitch fanassembly) and a turbomachine 103 (also referred to as the core of thegas turbine engine). In this example, the turbomachine 103 is atwo-spool turbomachine, which has a high-speed system and a low-speedsystem.

The high-speed system of the turbomachine 103, which is not shown inFIG. 1 , includes a high-pressure compressor, a high-pressure turbine, acombustor, and a high-speed shaft (also referred to as a “high-pressureshaft”) supported by bearings and connecting the high-pressurecompressor and the high-pressure turbine. The high-speed shaft,components of the high-pressure compressor, and components of thehigh-pressure turbine all rotate around a centerline axis 112 of the gasturbine engine 100. The high-pressure compressor (or at least therotating components thereof), the high-pressure turbine (or at least therotating components thereof), and the high-speed shaft may becollectively referred to as a high-pressure spool of the gas turbineengine 100. The combustor is located between the high-pressurecompressor and the high-pressure turbine. The combustor receives amixture of fuel and air and provides a flow of combustion gases throughthe high-pressure turbine for driving the high-pressure spool. Thehigh-pressure compressor, the high-pressure turbine, and the combustortogether define an engine core of the turbomachine 103.

The low-speed system of the turbomachine 103 includes a low-pressureturbine 120, a low-pressure compressor or booster 121, and a low-speedshaft 122 (also referred to as a “low-pressure shaft”) extending betweenand connecting the booster 121 and the low-pressure turbine 120. In someembodiments, the low-speed shaft 122 may extend further along thecenterline axis 112 than is shown in FIG. 1 . The low-pressure turbine120 is sometimes referred to as the engine's power turbine. Thelow-pressure turbine 120 converts kinetic energy contained in the hotgas exiting from the high-pressure turbine into mechanical shaft energy(e.g., of the low-speed shaft 122), which drives the booster 121 and fanblades 124 either directly or through a gearbox.

As shown in FIG. 1 , the gas turbine engine 100 defines an axialdirection A (extending parallel to the centerline axis 112), a radialdirection R that extends outward from, and inward to, the centerlineaxis 112 in a direction orthogonal to the axial direction A, and acircumferential direction C that extends three hundred sixty degrees(360°) around the centerline axis 112.

The low-speed shaft 122 is supported on bearings 123 a, 123 b, 123 c,123 d, which are mounted to support structures (not shown) of the gasturbine engine 100. At each position, only two bearings are shown inFIG. 1 for clarity, though more than two bearings, e.g., 3 or 4 bearingsforward and/or aft of the respective illustrated locations, may bearranged to support the low-speed shaft 122 at the respective positions,and may be evenly spaced or irregularly spaced depending on the geometryof the bearing supporting structure, and available space and clearances.

The low-speed shaft 122, components of the booster 121, and componentsof the low-pressure turbine 120 all rotate around the centerline axis112 of the gas turbine engine 100, in either the same direction or acounter-rotating direction as that of the high-pressure spool. Thebooster 121 (or at least the rotating components thereof), thelow-pressure turbine 120 (or at least the rotating components thereof),and the low-speed shaft 122 may collectively be referred to as alow-pressure spool 400 of the gas turbine engine 100, and is furtherdescribed in FIG. 4 .

The fan assembly 102 includes an array of fan blades 124 extendingradially outward from a rotor disc 126. The rotor disc 126 is covered bya rotatable fan hub 127 aerodynamically contoured to promote an airflowthrough array of fan blades 124. The gas turbine engine 100 has anintake side 128 and an exhaust side 130.

The turbomachine 103 is generally encased in a cowl 131. Moreover, itwill be appreciated that the cowl 131 defines at least in part an inlet132 of the turbomachine 103 and an exhaust 135 of the turbomachine 103,and includes a turbomachinery flow path extending between the inlet 132and the exhaust 135. For the embodiment shown in FIG. 1 , the inlet 132has an annular or an axisymmetric three hundred sixty-degreeconfiguration, and provides a flow path for incoming atmospheric air toenter the turbomachine 103. Such a location may be advantageous for avariety of reasons, including management of icing performance as well asprotecting the inlet 132 from various objects and materials as may beencountered in operation.

For a ducted turbofan engine (FIG. 1 ) a nacelle or fan duct 140surrounds the array of fan blades 124. The nacelle 140 is supportedrelative to the turbomachine 103 by circumferentially spaced outletguide vanes 142. The portion of air entering the fan duct 140 andbypassing the inlet 132 to the core engine is called the bypass airflow.In the embodiment of FIG. 1 , the bypass airflow flows through a bypassairflow passage 146 defined at a downstream end 144 of the nacelle 140.

For reference purposes, FIG. 1 depicts a forward or thrust directionwith arrow F, which in turn defines the forward and aft portions of thesystem. The fan assembly 102 is forward of the turbomachine 103 and theexhaust nozzle 135 is aft. The fan assembly 102 is driven by theturbomachine 103, and, more specifically, is driven by the low-pressureturbine 120.

In operation, a volume of air flows through fan assembly 102, and as thevolume of air passes across the array of fan blades 124, a first portionof air is directed or routed into the bypass airflow passage 146, and asecond portion of air is directed or routed into the inlet 132 and alongthe turbomachinery flow path. The ratio between the volume of the firstportion of air and the volume of the second portion of air is commonlyknown as a bypass ratio.

After entering the inlet 132, the second portion of air enters thebooster 121 and the high-pressure compressor (not shown in FIG. 1 ). Thehighly compressed air proceeds along the turbomachinery flow path and isdelivered to the combustor (not shown in FIG. 1 ), where the compressedair is mixed with fuel and burned to provide combustion exhaust gases.The exhaust from the combustor drives the high-pressure turbine (notshown in FIG. 1 ) and the low-pressure turbine 120, and the low-pressureturbine 120 drives the fan assembly 102 via the low-speed shaft 122.

The combustion exhaust gases are subsequently routed through the exhaust135 to provide propulsive thrust. Simultaneously, the pressure of thefirst portion of air is substantially increased as the first portion ofair is routed through the bypass airflow passage 146 before beingexhausted from a fan exhaust 148 at a downstream end 144, also providingpropulsive thrust. In such a manner, the fan blades 124 of the fanassembly 102 are driven to rotate around the centerline axis 112 andgenerate thrust to propel the gas turbine engine 100, and, hence, anaircraft to which it is mounted, in the forward direction F. Otherconfigurations are possible and contemplated within the scope of thepresent disclosure, such as what may be termed a “pusher” configurationembodiment in which the turbomachine 103 is located forward of the fanassembly 102.

As shown, the gas turbine engine 100 in the embodiment shown in FIG. 1has a direct drive configuration in which the low-speed shaft 122 isdirectly coupled to the rotor disc 126 and thereby rotates the fanassembly 102 at the same rotational speed as the low-pressure spool.Alternatively, in some embodiments, the turbomachine 103 includes apower gearbox (not shown in FIG. 1 ), and the fan assembly 102 isindirectly driven by the low-pressure spool of the turbomachine 103across the power gearbox. The power gearbox may include a gearset fordecreasing a rotational speed of the low-pressure spool relative to thelow-pressure turbine 120, such that the fan assembly 102 may rotate at aslower rotational speed than does the low-pressure spool.

FIG. 2 shows a schematic, cross-sectional view of a ducted,indirect-drive, gas turbine engine 200, also referred to as turbineengine 200, taken along a centerline axis 212 of the gas turbine engine200, according to an embodiment of the present disclosure. The gasturbine engine 200, also referred to herein as a turbine engine 200, issimilar in some respects to the gas turbine engine 100 discussed abovewith respect to FIG. 1 , and like reference numerals have been used torefer to the same or similar components. Parts omitted from FIG. 1 forclarity are shown and described with respect to FIG. 2 and, thus, theparts referenced, but not shown, in FIG. 1 may be the same or similarthose shown and described with respect to FIG. 2 . Likewise, partsomitted from the description of FIG. 2 for clarity are shown anddescribed with respect to FIG. 1 , and thus, the parts depicted but notdescribed may be the same as, or similar to, the parts described withrespect to FIG. 1 .

As shown in FIG. 2 , the turbine engine 200 includes, in downstreamserial flow relationship, a fan section 214 including a fan 202, acompressor section 216 including a booster or low-pressure (LP)compressor 221 and a high-pressure (HP) compressor 218, a combustionsection 228 including a combustor 230, a turbine section 233 includingan HP turbine 234, and an LP turbine 220, and an exhaust section 238.

The fan section 214 includes a fan casing 240, which is secured to anacelle (FIG. 1 ) surrounding the fan 202. The fan 202 includes aplurality of fan blades 224 disposed radially about the centerline axis212. The HP compressor 218, the combustor 230, and the HP turbine 234form an engine core 244 of the turbine engine 200, which generatescombustion gases. The engine core 244 is surrounded by a core casing231, which is coupled to the fan casing 240. The casing 240 is supportedrelative to the turbomachine by circumferentially spaced outlet guidevanes 282.

A high-speed shaft 248 is disposed coaxially about the centerline axis212 of the turbine engine 200 and drivingly connects the HP turbine 234to the HP compressor 218. A low-speed shaft 222, which is disposedcoaxially about the centerline axis 212 of the turbine engine 200 andwithin the larger diameter annular high-speed shaft 248, drivinglyconnects the LP turbine 220 to the LP compressor 221 and the fan 202(either directly or through a gearbox assembly 250). The high-speedshaft 248 and the low-speed shaft 222 are rotatable about the centerlineaxis 212.

The LP compressor 221 and the HP compressor 218, respectively, include arespective plurality of compressor stages 252, 254, in which arespective set of compressor blades 256, 258 rotate relative to arespective set of compressor vanes 260, 262 to compress or pressurizegas entering through the inlet 232. Referring now only to the HPcompressor 218, a single compressor stage 254 includes multiplecompressor blades 258 provided on a rotor disk 261 (or blades and diskare integrated together, referred to as a blisk). A compressor bladeextends radially outwardly relative to the engine centerline 212, from ablade platform to a blade tip. Compressor vanes 262 are positionedupstream/downstream of and adjacent to rotating compressor blades 258.The disk 261 for a stage of compressor blades 258 is mounted to thehigh-speed shaft 248 (HPC). A stage of the HPC refers to a single diskof rotor blades or both the rotor blades and adjacent stator vanes (itis understood that either meaning can apply within the context of thisdisclosure without loss of clarity).

The HP turbine 234 has one or two stages 264. In a single turbine stage264 turbine blades 268 are provided on a rotor disk 271. A turbine bladeextends radially outwardly relative to the centerline axis 212, from ablade platform to a blade tip. The HP turbine 234 can also include astator vane 272. The HP turbine 234 may have both an upstream nozzleadjacent the combustor exit and an exit nozzle aft of the rotor, or anozzle upstream of rotor blades or downstream of the rotor blades.

Air exiting the HP turbine 234 enters the LP turbine or power turbine220, which has a plurality of stages of rotating blades 270. The LPturbine 220 can have three, four, five or six stages. In a single LPturbine stage 266 (containing a plurality of blades coupled to the LPshaft 222) a turbine blade is provided on a rotor disk (connected to theLP shaft 222) and extends radially outwardly relative to the centerlineaxis 212, from a blade platform to a blade tip. The LP turbine 220 canalso include a stator vane 274. The LP turbine 220 may have both anupstream nozzle and an exit nozzle aft of a stage, followed by theengine's exhaust nozzle 238.

The turbine engine 200 of FIG. 2 operates in a similar manner as theengine of FIG. 1 . Airflow exiting the fan section 214 is split suchthat a portion of the airflow is channeled into an inlet 232 to the LPcompressor 221, which then supplies pressurized airflow to the HPcompressor 218, which further pressurizes the air. The pressurizedairflow from the HP compressor 218 is mixed with fuel in the combustor230 and ignited, thereby generating combustion gases. Some work isextracted from the combustion gases by the HP turbine 234, which drivesthe HP compressor 218 to produce a self-sustaining combustion. Thecombustion gases discharged from the HP turbine enter the LP turbine220, which extracts additional work to drive the LP compressor 221 andthe fan 202 (directly or through a gearbox assembly 250). The gasdischarged from the LP turbine exits through the exhaust nozzle 238.

Some of the air supplied by the fan 202 bypasses the engine core 244 andis used for cooling of portions, especially hot portions, of the turbineengine 200, and/or used to cool or power other aspects of the aircraft.In the context of the turbine engine 200, the hot portions refer to avariety of portions of the turbine engine 200 downstream of thecombustion section 228 (e.g., the turbine section 233). Other sources ofcooling fluid include, but are not limited to, fluid discharged from theLP compressor 221 or the HP compressor 218.

The gas turbine engines 100 and 200 depicted in FIG. 1 and FIG. 2 are byway of example only. In other embodiments, the gas turbine engine mayhave any other suitable configuration, including, for example, any othersuitable number or configurations of shafts or spools, fan blades,turbines, compressors, or combination thereof. The gearbox assembly mayhave any suitable configuration, including, for example, a star gearconfiguration, a planet gear configuration, a single-stage, amulti-stage, epicyclic, non-epicyclic, etc., as detailed further below.The gearbox may have a gear ratio in a range of 3:1 to 4:1, 3:5 to 4:1,3.25:1 to 3.5:1, or 4:1 to 5:1. The fan assembly may be any suitablefixed-pitched assembly or variable-pitched assembly. The gas turbineengine may include additional components not shown in FIG. 1 , such asrotor blades, stator vanes, etc. The fan assembly may be configured inany other suitable manner (e.g., as a fixed pitch fan) and further maybe supported using any other suitable fan frame configuration. Aspectsof the present disclosure may be incorporated into any other suitableturbine engine, including, but not limited to, turbofan engines, propfanengines, turbojet engines, turboprop, and turboshaft engines.

FIG. 3 shows a schematic view of an unducted, three-stream, gas turbineengine 310 for an aircraft, that may incorporate one or more embodimentsof the present disclosure. The gas turbine engine 310 is a “three-streamengine” in that its architecture provides three distinct streams(labeled S1, S2, and S3) of thrust-producing airflow during operation,as detailed further below.

As shown in FIG. 3 , the gas turbine engine 310 defines an axialdirection A, a radial direction R, and a circumferential direction C.Moreover, the gas turbine engine 310 defines a centerline axis 312 thatextends along the axial direction A. In general, the axial direction Aextends parallel to the centerline axis 312, the radial direction Rextends outward from, and inward to, the centerline axis 312 in adirection orthogonal to the axial direction A, and the circumferentialdirection C extends three hundred sixty degrees (360°) around thecenterline axis 312. The gas turbine engine 310 extends between aforward end 314 and an aft end 316, e.g., along the axial direction A.

The gas turbine engine 310 includes a core engine 320 and a fan assembly350 positioned upstream thereof. Generally, the core engine 320includes, in serial flow order, a compressor section, a combustionsection, a turbine section, and an exhaust section. Particularly, asshown in FIG. 3 , the core engine 320 includes an engine core 318 and acore cowl 322 that annularly surrounds the core engine 320. The coreengine 320 and the core cowl 322 define a core inlet 324 having anannular shape. The core cowl 322 further encloses and supports alow-pressure (LP) compressor 326 (also referred to as a booster) forpressurizing the air that enters the core engine 320 through core inlet324. A high-pressure (HP) compressor 328 receives pressurized air fromthe LP compressor 326 and further increases the pressure of the air. Thepressurized air flows downstream to a combustor 330 where fuel isinjected into the pressurized air and ignited to raise the temperatureand the energy level of the pressurized air, thereby generatingcombustion gases.

The combustion gases flow from the combustor 330 downstream to ahigh-pressure (HP) turbine 332. The HP turbine 332 drives the HPcompressor 328 through a first shaft, also referred to as ahigh-pressure (HP) shaft 336 (also referred to as a “high-speed shaft”).In this regard, the HP turbine 332 is drivingly coupled with the HPcompressor 328. Together, the HP compressor 328, the combustor 330, andthe HP turbine 332 define the engine core 318. The combustion gases thenflow to a power turbine or low-pressure (LP) turbine 334. The LP turbine334 drives the LP compressor 326 and components of the fan assembly 350through a second shaft, also referred to as a low-pressure (LP) shaft338 (also referred to as a “low-speed shaft”). In this regard, the LPturbine 334 is drivingly coupled with the LP compressor 326 andcomponents of the fan assembly 350. The low-speed shaft 338 is coaxialwith the high-speed shaft 336 in the embodiment of FIG. 3 . Afterdriving each of the HP turbine 332 and the LP turbine 334, thecombustion gases exit the core engine 320 through a core exhaust nozzle340. The core engine 320 defines a core flowpath, also referred to as acore duct 342, that extends between the core inlet 324 and the coreexhaust nozzle 340. The core duct 342 is an annular duct positionedgenerally inward of the core cowl 322 along the radial direction R.

The fan assembly 350 includes a primary fan 352. For the embodiment ofFIG. 3 , the primary fan 352 is an open rotor fan, also referred to asan unducted fan. However, in other embodiments, the primary fan 352 maybe ducted, e.g., by a fan casing or a nacelle circumferentiallysurrounding the primary fan 352. The primary fan 352 includes an arrayof fan blades 354 (only one shown in FIG. 3 ). The fan blades 354 arerotatable about the centerline axis 312 via a fan shaft 356. As shown inFIG. 3 , the fan shaft 356 is coupled with the low-speed shaft 338 via aspeed reduction gearbox, also referred to as a gearbox assembly 355,e.g., in an indirect-drive configuration. The gearbox assembly 355 isshown schematically in FIG. 3 . The gearbox assembly 355 includes aplurality of gears for adjusting the rotational speed of the fan shaft356 and, thus, the primary fan 352 relative to the low-speed shaft 338to a more efficient rotational fan speed. The gearbox assembly may havea gear ratio of 4:1 to 12:1, or 7:1 to 12:1, or 4:1 to 10:1, or 5:1 to9:1, or 6:1 to 9:1, and may be configured in an epicyclic star or planetgear configuration. The gearbox may be a single stage or compoundgearbox.

The fan blades 354 can be arranged in equal spacing around thecenterline axis 312. Each fan blade 354 has a root and a tip and a spandefined therebetween. Each fan blade 354 defines a central blade axis357. For the embodiment of FIG. 3 , each fan blade 354 of the primaryfan 352 is rotatable about their respective central blade axis 357,e.g., in unison with one another. One or more actuators 358 arecontrolled to pitch the fan blades 354 about their respective centralblade axis 357. In other embodiments, each fan blade 354 is fixed or isunable to be pitched about the central blade axis 357.

The fan assembly 350 further includes a fan guide vane array 360 thatincludes fan guide vanes 362 (only one shown in FIG. 3 ) disposed aroundthe centerline axis 312. For the embodiment of FIG. 3 , the fan guidevanes 362 are not rotatable about the centerline axis 312. Each fanguide vane 362 has a root and a tip and a span defined therebetween. Thefan guide vanes 362 can be unshrouded as shown in FIG. 3 or can beshrouded, e.g., by an annular shroud spaced outward from the tips of thefan guide vanes 362 along the radial direction R. Each fan guide vane362 defines a central vane axis 364. For the embodiment of FIG. 3 , eachfan guide vane 362 of the fan guide vane array 360 is rotatable abouttheir respective central vane axis 364, e.g., in unison with oneanother. One or more actuators 366 are controlled to pitch the fan guidevanes 362 about their respective central vane axis 364. In otherembodiments, each fan guide vane 362 is fixed or is unable to be pitchedabout the central vane axis 364. The fan guide vanes 362 are mounted toa fan cowl 370.

The fan cowl 370 annularly encases at least a portion of the core cowl322 and is generally positioned outward of the core cowl 322 along theradial direction R. Particularly, a downstream section of the fan cowl370 extends over a forward portion of the core cowl 322 to define a fanflowpath, also referred to as a fan duct 372. Incoming air entersthrough the fan duct 372 through a fan duct inlet 376 and exits througha fan exhaust nozzle 378 to produce propulsive thrust. The fan duct 372is an annular duct positioned generally outward of the core duct 342along the radial direction R. The fan cowl 370 and the core cowl 322 areconnected together and supported by a plurality of struts 374 (only oneshown in FIG. 3 ) that extend substantially radially and arecircumferentially spaced about the centerline axis 312. The plurality ofstruts 374 are each aerodynamically contoured to direct air flowingthereby. Other struts in addition to the plurality of struts 374 can beused to connect and support the fan cowl 370 and/or the core cowl 322.

The gas turbine engine 310 also defines or includes an inlet duct 380.The inlet duct 380 extends between an engine inlet 382 and the coreinlet 324 and the fan duct inlet 376. The engine inlet 382 is definedgenerally at the forward end of the fan cowl 370 and is positionedbetween the primary fan 352 and the fan guide vane array 360 along theaxial direction A. The inlet duct 380 is an annular duct that ispositioned inward of the fan cowl 370 along the radial direction R. Airflowing downstream along the inlet duct 380 is split, not necessarilyevenly, into the core duct 342 and the fan duct 372 by a splitter 384 ofthe core cowl 322. The inlet duct 380 is wider than the core duct 342along the radial direction R. The inlet duct 380 is also wider than thefan duct 372 along the radial direction R.

The fan assembly 350 also includes a mid-fan 386. The mid-fan 386includes a plurality of mid-fan blades 388 (only one shown in FIG. 3 ).The plurality of mid-fan blades 388 are rotatable, e.g., about thecenterline axis 312. The mid-fan 386 is drivingly coupled with the LPturbine 334 via the low-speed shaft 338. The plurality of mid-fan blades388 can be arranged in equal circumferential spacing about thecenterline axis 312. The plurality of mid-fan blades 388 are annularlysurrounded (e.g., ducted) by the fan cowl 370. In this regard, themid-fan 386 is positioned inward of the fan cowl 370 along the radialdirection R. The mid-fan 386 is positioned within the inlet duct 380upstream of both the core duct 342 and the fan duct 372. A ratio of aspan of a blade 354 to that of a mid-fan blade 388 (a span is measuredfrom a root to tip of the respective blade) is greater than 2 and lessthan 10, to achieve the desired benefits of the third stream (S3),particularly the additional thrust it offers to the engine, which canenable a smaller diameter blade 354 (benefits engine installation).

Accordingly, air flowing through the inlet duct 380 flows across theplurality of mid-fan blades 388 and is accelerated downstream thereof.At least a portion of the air accelerated by the mid-fan blades 388flows into the fan duct 372 and is ultimately exhausted through the fanexhaust nozzle 378 to produce propulsive thrust. Also, at least aportion of the air accelerated by the plurality of mid-fan blades 388flows into the core duct 342 and is ultimately exhausted through thecore exhaust nozzle 340 to produce propulsive thrust. Generally, themid-fan 386 is a compression device positioned downstream of the engineinlet 382. The mid-fan 386 is operable to accelerate air into the fanduct 372, also referred to as a secondary bypass passage.

During operation of the gas turbine engine 310, an initial or incomingairflow passes through the fan blades 354 of the primary fan 352 andsplits into a first airflow and a second airflow. The first airflowbypasses the engine inlet 382 and flows generally along the axialdirection A outward of the fan cowl 370 along the radial direction R.The first airflow accelerated by the fan blades 354 passes through thefan guide vanes 362 and continues downstream thereafter to produce aprimary propulsion stream or first thrust stream S1. A majority of thenet thrust produced by the gas turbine engine 310 is produced by thefirst thrust stream S1. The second airflow enters the inlet duct 380through the engine inlet 382.

The second airflow flowing downstream through the inlet duct 380 flowsthrough the plurality of mid-fan blades 388 of the mid-fan 386 and isconsequently compressed. The second airflow flowing downstream of themid-fan blades 388 is split by the splitter 384 located at the forwardend of the core cowl 322. Particularly, a portion of the second airflowflowing downstream of the mid-fan 386 flows into the core duct 342through the core inlet 324. The portion of the second airflow that flowsinto the core duct 342 is progressively compressed by the LP compressor326 and the HP compressor 328 and is ultimately discharged into thecombustion section. The discharged pressurized air stream flowsdownstream to the combustor 330 where fuel is introduced to generatecombustion gases or products.

The combustor 330 defines an annular combustion chamber that isgenerally coaxial with the centerline axis 312. The combustor 330receives pressurized air from the HP compressor 328 via a pressurecompressor discharge outlet. A portion of the pressurized air flows intoa mixer. Fuel is injected by a fuel nozzle (omitted for clarity) to mixwith the pressurized air thereby forming a fuel-air mixture that isprovided to the combustion chamber for combustion. Ignition of thefuel-air mixture is accomplished by one or more igniters (omitted forclarity), and the resulting combustion gases flow along the axialdirection A toward, and into, a first stage turbine nozzle of the HPturbine 332. The first stage turbine nozzle 333 is defined by an annularflow channel that includes a plurality of radially extending,circumferentially spaced nozzle vanes 335 that turn the combustion gasesso that they flow angularly and impinge upon first stage turbine bladesof the HP turbine 332. The combustion gases exit the HP turbine 332 andflow through the LP turbine 334 and exit the core duct 342 through thecore exhaust nozzle 340 to produce a core air stream, also referred toas a second thrust stream S2. As noted above, the HP turbine 332 drivesthe HP compressor 328 via the high-speed shaft 336, and the LP turbine334 drives the LP compressor 326, the primary fan 352, and the mid-fan386 via the low-speed shaft 338.

The other portion of the second airflow flowing downstream of themid-fan 386 is split by the splitter 384 into the fan duct 372. The airenters the fan duct 372 through the fan duct inlet 376. The air flowsgenerally along the axial direction A through the fan duct 372 and isultimately exhausted from the fan duct 372 through the fan exhaustnozzle 378 to produce a third stream, also referred to as a third thruststream S3.

The third thrust stream S3 is a secondary air stream that increasesfluid energy to produce a minority of total propulsion system thrust. Insome embodiments, a pressure ratio of the third stream is higher thanthat of the primary propulsion stream (e.g., a bypass or a propellerdriven propulsion stream). The thrust may be produced through adedicated nozzle or through mixing of the secondary air stream with theprimary propulsion stream or a core air stream, e.g., into a commonnozzle. In certain embodiments, an operating temperature of thesecondary air stream is less than a maximum compressor dischargetemperature for the engine. Furthermore in certain embodiments, aspectsof the third stream (e.g., airstream properties, mixing properties, orexhaust properties), and thereby a percent contribution to total thrust,are passively adjusted during engine operation or can be modifiedpurposefully through use of engine control features (such as fuel flow,electric machine power, variable stators, variable inlet guide vanes,valves, variable exhaust geometry, or fluidic features) to adjust or toimprove overall system performance across a broad range of potentialoperating conditions.

The gas turbine engine 310 depicted in FIG. 3 is by way of example only.In other embodiments, the gas turbine engine 310 may have any othersuitable configuration. For example, in other embodiments, the primaryfan 352 may be configured in any other suitable manner (e.g., as a fixedpitch fan) and further may be supported using any other suitable fanframe configuration. In other embodiments, the primary fan 352 can beducted by a fan casing or a nacelle such that a bypass passage isdefined between the fan casing and the fan cowl 370. Moreover, in otherembodiments, any other suitable number or configuration of compressors,turbines, shafts, or a combination thereof may be provided. In stillother embodiments, aspects of the present disclosure may be incorporatedinto any other suitable turbine engine, such as, for example, turbofanengines, propfan engines, turbojet engines, turboprop, turboshaftengines, and/or turbine engines defining two streams (e.g., a bypassstream and a core air stream).

Further, for the depicted embodiment of FIG. 3 , the gas turbine engine310 includes an electric machine 390 (motor-generator) operably coupledwith a rotating component thereof. In this regard, the gas turbineengine 310 is a hybrid-electric propulsion machine. Particularly, asshown in FIG. 3 , the electric machine 390 is operatively coupled withthe low-speed shaft 338. The electric machine 390 can be mechanicallyconnected to the low-speed shaft 338, either directly, or indirectly,e.g., by way of a gearbox assembly 392 (shown schematically in FIG. 3 ).Further, although in this embodiment the electric machine 390 isoperatively coupled with the low-speed shaft 338 at an aft end of thelow-speed shaft 338, the electric machine 390 can be coupled with thelow-speed shaft 338 at any suitable location or can be coupled to otherrotating components of the gas turbine engine 310, such as thehigh-speed shaft 336 or the low-speed shaft 338. For instance, in someembodiments, the electric machine 390 can be coupled with the low-speedshaft 338 and positioned forward of the mid-fan 386 along the axialdirection. In some embodiments the engine of FIG. 2 also includes anelectric machine coupled to the LP shaft and located in the engine'stail cone.

In some embodiments, the electric machine 390 can be an electric motoroperable to drive or motor the low-speed shaft 338, e.g., during anengine burst. In other embodiments, the electric machine 390 can be anelectric generator operable to convert mechanical energy into electricalenergy. In this way, electrical power generated by the electric machine390 can be directed to various engine and/or aircraft systems. In someembodiments, the electric machine 390 can be a motor/generator with dualfunctionality. The electric machine 390 includes a rotor 394 and astator 396. The rotor 394 is coupled to the low-speed shaft 338 androtates with rotation of the low-speed shaft 338. In this way, the rotor394 rotates with respect to the stator 396, thereby generatingelectrical power. Although the electric machine 390 has been describedand illustrated in FIG. 3 as having a particular configuration, thepresent disclosure may apply to electric machines having alternativeconfigurations. For instance, the rotor 394 and/or the stator 396 mayhave different configurations or may be arranged in a different mannerthan illustrated in FIG. 3 .

FIG. 4 shows an enlarged view of a portion of the cross-sectional viewof FIG. 1 , that includes the low-pressure spool 400 according to someembodiments of the present disclosure. For example, a portion of thebooster 121 and a portion of the low-pressure turbine 120 are shownmounted to the low-speed shaft 122 of the turbomachine 103, which inthis example is a two-spool turbomachine. Alternatively, the low-speedshaft 122 may be an intermediate shaft in a three-spool turbomachine(not shown). The low-speed shaft 122 is supported by at least bearings123 a to 123 d, which are located at mounting points 405 a, 405 bassociated with the booster 121 location and a low-pressure turbine 120location, respectively, for providing shaft rotational support at theselocations. In the example of FIG. 4 , bearings 123 a, 123 b, 123 c, and123 d are all positioned inside of the mounting points 405 a and 405 b,which is referred to as an inbound bearing layout, or alternativelyreferred to as an overhung configuration for the booster 121 andlow-pressure turbine 120. If the bearings were positioned outside of themounting point 405 b, then that would be referred to as an outboundlayout. The bearings 123 a to 123 d can, however, be positioned at anypoint along the low-speed shaft 122, and may both be inbound, both beoutbound, or one inbound and the other outbound.

The low-speed shaft 122 has a length “L” (indicated by arrow 408) and anouter diameter “D” (indicated by arrow 410). The length L is alsoreferred to as L_(MSR) and the outer diameter D is also referred toD_(MSR), as detailed further below. The low-speed shaft 122 can behollow, with an inner diameter “d” indicated by arrow 411). In caseswhen the diameter of the low-speed shaft 122 varies along the length L,the outer diameter “D” and the inner diameter “d” may be defined at amidpoint of the low-speed shaft 122 (also referred to as the midshaft415). The thickness may be defined as the thickness of the walls of thelow-speed shaft 122 in embodiments in which the low-speed shaft 122 ishollow. A difference between a stated outer diameter D and innerdiameter d of the low-speed shaft 122 may be understood as the shaft'swall thickness. In cases when the wall thickness varies along the lengthof the low-speed shaft 122, the thickness may be defined as thedifference between the inner diameter and the outer diameter at themidshaft 415.

In some embodiments, the length L can be understood as the portion ofthe low-speed shaft 122 between the bearings 123 a to 123 d and/or themounting points 405 a, 405 b of engine components such as the booster121 and the low-pressure turbine 120. For example, in the two-bearingarrangement of FIG. 4 , the length L may be measured as the distancebetween midpoints of the bearings 123 a to 123 b, as indicated by thedashed vertical lines and arrow 408. For a four-bearing arrangement,there may be additional bearings along the shaft, in which case thelength L may be measured as the distance between the midpoints of aninnermost pair of bearings, or the distance between pairs or othergroupings of bearings. In some embodiments, the length may be measuredrelative to specific bearings associated with specific engine componentssuch as the booster 121 and the low-pressure turbine 120.

During operation, the low-speed shaft 122 rotates with a rotationalspeed that can be expressed in either rotations per minute (RPM), or asan outer diameter (OD) speed expressed in units of linear velocity, suchas feet per second (ft/sec). The rotational stability of the low-speedshaft 122 relative to its operational range may be characterized by theresonance frequency of the fundamental or first order bending mode. Whenan operational speed is the same as this resonance frequency, the shaftis operating at its critical speed. The low-speed shaft 122, whensupported by bearings 123 a to 123 d, has a mode shape for thisfirst-order bending mode that may be generally described as ahalf-sinusoid, with a midshaft 415 location undergoing maximumdisplacement (indicated by arrow 420, which is exaggerated for clarityand is not to scale) and, therefore, having a maximum kinetic energy ofdisplacement relative to other portions of the low-speed shaft 122. Thefundamental mode shape is illustrated by dashed line 425 extending frombearing 123 c to bearing 123 d in FIG. 4 , though this is only half ofthe amplitude of oscillation. This unstable mode is a standing waveacross the length L of the low-speed shaft 122. The maximum deflectionoccurs when the excitation source has a periodicity or cyclic componentnear to the fundamental frequency. Since the bending mode is not activeat the location of the innermost bearings 123 a to 123 d for thelow-speed shaft 122, the instability cannot be mitigated with the use ofbearing dampers. When an engine is designed, the shaft speed expected toproduce the highest deflection or instability at the midshaft is theshaft speed that equals the critical speed.

If the critical speed of the shaft critical speed falls within thestandard operational range, i.e., if the critical speed is below theredline speed or the low-speed shaft 122 is a supercritical shaft, thenduring routine operation, the low-speed shaft 122 may at times operateat or pass through the critical speed, which induces an unstablecondition. Even if the engine is operated at the critical speedtemporarily, there is a possibility of undetected vibration, whirlinstability, and some likelihood of damage. For low vibration andstability, it is preferable to have an operating range free of anyintervening critical speeds.

There is a desire to pursue engines capable of operating at higherredline speeds. This pursuit of higher operating speeds requires thatthe low-speed shaft 122 have a higher strength to weight characteristicif it is also desired that the shaft remain subcritical. The inventorssought this end result—higher speed shafts while remaining subcritical.To this end, a large number of engine designs were evaluated. Dependingon the architecture, the positions and numbers of bearings relative tomounting points 405 a, 405 b were varied, and the resulting impact, notonly on the critical speed but also the feasibility of suchconfigurations given competing requirements (clearance, spacing, sumplocations, oil supply lines), were taken into consideration, as will bereadily apparent in view of the disclosure. A discussion of theseembodiments follows. In the following discussion, strength to weightratio is represented as E/rho, calculated as the ratio of Young'smodulus E for the material (expressed, for example, in pounds per squarefoot) divided by the density rho (expressed, for example, in pounds percubic inch). The shaft bending mode is represented as the criticalrotational speed expressed in rotations per minute (RPM), though itcould alternatively be expressed as the fundamental frequency of thebending mode in Hertz.

In some embodiments, high strength steel alloys, advanced materials,composite materials, and combinations thereof, were contemplated. Forexample, high strength-to-weight ratio materials such as titanium boride(TiB) or a titanium metal matrix composite (TiMMC), provided 30% to 50%increased strength-to-weight ratio relative to steel or titanium alloys.In addition, coatings with materials such as graphene were found toimprove strength by a factor of two in lab tests, without impactingweight. These types of changes in material composition may becharacterized in some embodiments by the ratio of E/rho.

FIG. 5A shows a cross-sectional view of a steel shaft 505, with astandard hollow interior 506 surrounded by a steel layer 507, andgeometry defined by a length L, outer diameter D, inner diameter d, etc.

FIG. 5B shows a cross-sectional view of an example of a composite shaft510, with identical geometry to the steel shaft 505. Rather than beingcomposed entirely of steel, the composite shaft 510 has an inner layer515 surrounding a hollow interior 517, a middle layer 520, and an outercoating 525, all of different materials. The middle layer 520 in thisexample is also steel, though in other embodiments the composite shaftcould use no steel at all, or have a different layer be steel.

For example, both the steel shaft 505 and the composite shaft 510 havelength L of seventy-six inches and outer diameter of three inches, alongwith a standard inbound two-bearings configuration as depicted in FIG. 4. The fundamental frequency of the unstable mode for the steel shaft 505is eighty Hertz (Hz), whereas the fundamental frequency for thecomposite shaft 510 is ninety Hz.

In other embodiments, more layers or fewer layers may be used. Some orall of these layers and coatings may be of numerous alternativematerials to steel, including but not limited to TiB, TiMMC, othermetals and metal matrix composites, silicon carbide (SiC), siliconcarbide reinforced metals or alloys (e.g., SiC-MMC), aluminum alloys,graphene, or combinations thereof. The concepts of the presentdisclosure are not limited by the particular materials used for thelayers and coatings. For the composite shaft 510, the critical speedcorresponding to the unstable mode is increased relative to the(otherwise identical) steel shaft 505, which means that relative to thesteel shaft 505, the composite shaft 510 can attain a higher rotationalspeed before reaching the critical speed.

Depending on the type of composite materials chosen and the relativethickness and arrangement of the layers, the ratio of stiffness toweight can be modified, and therefore, the critical speed can beincreased. The inventors conceived of a variety of embodiments resultingfrom the selection of different composite materials, thicknesses, andbearings configurations to allow for operation at higher speed. Two suchembodiments are listed in TABLE 1. These embodiments were considered aspossible designs that could increase the shaft stiffness to weight ratioin such a way to be compatible with engine architecture and withoutrequiring modifications or limitations on the targeted operating rangefor a subcritical shaft.

TABLE 1 E/rho Teff Mode Embodiment L (in) D (in) Bearing type (in⁻¹)(in) (RPM) 1 82.2 2.74 2-bearing outbound 1.00E+08 0.35 4181 2 60.6 2.75inbound OTM 1.27E+08 0.35 10263 3 82.2 2.74 outbound OTM 1.27E+08 0.356915

Embodiment 1 was evaluated using a high strength steel alloy and anoutbound bearing layout. Embodiments 2 and 3 were evaluated with acomposite material instead of steel alloy. Embodiment 2 uses overturningmoment (OTM) bearings with an inbound bearing layout that is differentfrom the layout used by Embodiment 1. Embodiment 3 uses OTM bearingswith an outbound bearing layout that is similar to that used byEmbodiment 1. These bearing types and layouts are described in furtherdetail below with reference to FIG. 7A, FIG. 7B, and TABLE 3. The valuesshown in TABLE 1 illustrate that Embodiments 2 and 3 achieve a higherstrength-to-weight ratio (E/rho) when using a composite material,instead of the steel alloy used in Embodiment 1. As a result of thesedifferences, the shaft mode critical speed occurs at 4181 RPM forEmbodiment 1, at 10263 RPM for Embodiment 2 and at 6915 for Embodiment3.

The inventors also modified the shaft thickness along its length, toevaluate the effect on critical speed for a strength to weight ratio ofE/rho that is not constant along the length L, and for differentsuitable materials. An example of a shaft with a uniform E/rho along itslength L is shown in FIG. 6A, and examples of shafts having variableE/rho are shown in FIG. 6B and FIG. 6C.

FIG. 6A conceptually shows a cross-sectional view of a uniform shaft 605with a constant diameter and thickness. In this example, the uniformshaft 605 has a length L of seventy-six inches. The outer diameter D ofthe uniform shaft 605 is 3.0 inches. The uniform shaft 605 is hollow,with a constant wall thickness of 0.2 inch and corresponding constantinner radius of 1.3 inches along its length. For this example of auniform shaft 605, and a two-bearing outbound configuration such as inFIG. 4 , the fundamental frequency of the unstable mode is eighty Hz.

FIG. 6B conceptually shows a cross-sectional view of a concave shaft 610with a constant outer diameter D and a variable thickness. Forcomparison, the uniform shaft 605 and the concave shaft 610 have thesame material (e.g., hollow steel), bearings (outbound), and length(seventy-six inches), with a constant outer radius of 1.5 inches alongits length. The outer diameter D of the concave shaft 610 is, therefore,3.0 inches. Unlike the uniform shaft 605, however, the concave shaft 610has a wall thickness of 0.3 inch at the ends 612, 614 (e.g., at thebearings, which are not shown in FIGS. 6A to 6C), and a thinner wallthickness of 0.15 inches in the midshaft region 615. This results in aninner radius of 1.35 inches in the midshaft region 615 and a smallerinner radius of 1.2 inches at the ends 612, 614. The concave shaft 610therefore has a reduced mass density in the midshaft region 615. Toachieve the resulting concave profile, various methods may be used tomanufacture the concave shaft 610, such as a bottle boring technique.

FIG. 6C conceptually shows a cross-sectional view of a convex shaft 620with a variable outer diameter D and a variable thickness. Forcomparison, the uniform shaft 605 and the convex shaft 620 have the samematerial (e.g., hollow steel), bearings (outbound), and length(seventy-six inches), with a constant inner radius of 1.2 inches alongits length. Unlike the uniform shaft 605, the convex shaft 620 has awall thickness of 0.3 inch at the ends 622, 624, and a thinner wallthickness of 0.15 inches in the midshaft region 625, just like theconcave shaft 610. Unlike the concave shaft 610, the convex shaft 620has an outer radius of 1.5 inches at the ends 622, 624, and a smallerouter radius of 1.35 inches in the midshaft region 625. The convex shaft620 also has a reduced mass density in the midshaft region 625.

Since the radius (and, therefore, the diameter) are variable over thelength of the convex shaft 620, the diameter D is defined in someembodiments as the diameter at the midshaft region 625, since this hasthe most relevance to the bending mode and undergoes maximum deflection.In the example of the convex shaft 620, the shaft outer diameter D is2.7 inches in the midshaft region 625. In other embodiments, forexample, embodiments when the radius has multiple minima and/or maxima,the diameter D may be defined at any of those minima or maxima. Toachieve the resulting convex profile, various methods may be used tomanufacture the convex shaft 620, such as external machining.

For both convex and concave thickness profiles, as well as types ofvariable thickness profiles, the thickness may be described using aneffective thickness value, Teff. For a uniform shaft the thickness wouldsimply be the difference between the outer diameter and the innerdiameter. When these values are variable over the length of the shaft,the effective thickness can be calculated as the difference between theeffective outer diameter and effective inner diameter. For example, theeffective thickness may be defined at the midshaft in some embodiments.

With variable thickness, in some embodiments the concave shaft 610 andthe convex shaft 620 can have twenty-five to thirty percent less weightthan the uniform shaft 605 in the midshaft region 615 and 625,respectively. Note that the variation in thickness need not becontinuous, for example a stepped change in geometry could also be used.As a result, the fundamental frequency of the unstable mode for both theconcave shaft 610 and the convex shaft 620 is increased to ninety Hz,which is higher than the eighty Hz fundamental frequency for the uniformshaft 605. In other words, the concave shaft 610 and the convex shaft620 can both attain a higher rotational speed than that of uniform shaft605, before reaching subcritical speeds.

The concave shaft 610 and the convex shaft 620 are examples of differentthickness profiles that may be used in some embodiments. Other thicknessprofiles are also contemplated, which reduce or increase the massdensity of the shaft in the midshaft region. The concepts of the currentdisclosure are not limited by the particular thickness profile used.

Depending on the thickness profile, the ratio of stiffness to weight canbe modified to produce significant changes in the critical speed.embodiments are listed in TABLE 2. These embodiments were considered aspossible designs that could modify the effective thickness in such a wayto be compatible with engine architecture and without requiringmodifications or limitations on the targeted operating range for asubcritical shaft.

TABLE 2 E/rho Teff Mode Embodiment L (in) D (in) Bearing type (in⁻¹)(in) (RPM) 4 60.6 2.75 inbound OTM 1.00E+08 0.35 9001 5 82.2 2.74outbound OTM 1.00E+08 0.35 6065 6 60.6 2.75 inbound OTM 1.00E+08 0.3210039 7 82.2 2.74 outbound OTM 1.00E+08 0.32 6942

Embodiments 4, 5, 6, and 7 all use a steel alloy material composition.Embodiments 4 and 6 use an inbound bearing layout with OTM bearings, andEmbodiments 5 and 7 use an outbound bearing layout with OTM bearings.Embodiments 4 and 5 are uniform shafts similar to the Example of FIG.6A. Embodiments 6 and 7, however, have a convex thickness profilesimilar to the example of FIG. 6C, having been manufactured with abottle boring manufacturing technique. The values shown in TABLE 2illustrate that Embodiments 6 and 7 achieve a lower effective thicknessTeff due to their convex profile, instead of the uniform profile forEmbodiments 4 and 5. As a result of these differences, the shaft modecritical speed occurs at 9001 RPM for Embodiment 4, and at 10039 RPM forEmbodiment 6. The shaft mode critical speed occurs at 6065 RPM forEmbodiment 5, and at 6942 RPM for Embodiment 7.

The inventors also conceived of a variety of shafts with modifiedbearing configurations. Bearings are used to provide transverse supportto the shaft along its length. Bearings may be ball-type bearings, whichhave a very small contact area with the shaft to provide less friction,or roller-type bearings, which have a large contact area with the shaftto provide increased rigidity and load bearing. Different types ofbearings may be mixed in various bearing layouts. According toadditional embodiments, different bearing layouts were considered, fordifferent combinations of uniform, convex, and concave shafts, orvarying shaft thickness profiles and material composition in order todetermine which combination would work best for a given architecture andneed, as well as taking into account competing engineering requirements.

A variety of combinations of bearing configurations were contemplated,such as embodiments when the number of bearings in duplex and/orstraddling position relative to engine components (e.g., a booster 721or a low-pressure turbine 720) were changed. Either or both of theengine components mounted to the shaft 722 may be straddled or overhung.It was found that these variations can improve the critical speed and/orbe more suitable to accommodate space limitations, lubrication resourcesor other architecture-imposed limitations. The embodiments includedlocating bearings at different inbound or outbound positions relative tothe mounting points 705 a, 705 b.

Specific bearing layouts were preferentially used in variousembodiments. These are now described in more detail, though the conceptsof the present disclosure are not limited by the particular number orarrangement of bearings described herein.

For example, FIG. 7A conceptually shows a low-pressure turbine 720 and abooster 721 mounted on a shaft 722 (e.g., a low-speed shaft) supportedby a four-bearing straddle configuration. Additional bearings locatedaround the circumference of the shaft 722 are omitted from FIG. 7A forclarity. In this system, one pair of bearings 723 a, 724 a straddle(i.e., placed forward and aft of) a mounting point 705 a of the booster721, and a second pair of bearings 723 b, 724 b straddle a mountingpoint 705 b of the low-pressure turbine 720. In this example, bearings724 a, 723 b, and 724 b are roller bearings, and bearing 723 a is a ballbearing, though these bearing types may vary in other embodiments. Thelength L for shaft 722 is represented in some embodiments as thedistance between the midpoints or centers of the innermost bearings 724a, 723 b. The four-bearing straddle layout is used in severalembodiments described with reference to TABLE 3.

As another example, FIG. 7B conceptually shows a low-pressure turbine720 and a booster 721 mounted on a shaft 722 supported by a four-bearingoutbound configuration. Additional bearings located around thecircumference of the shaft 722 are omitted from FIG. 7B for clarity.This system is similar to that of the straddle system shown in FIG. 7A,but differs in that bearings 723 a, 724 a are both placed forward ofmounting point 705 a of the booster 721, and bearings 723 b, 724 b areplaced aft of mounting point 705 b of the low-pressure turbine 720. Theshaft 722 may extend beyond bearings 723 b, 724 b. As in the example ofFIG. 7A, bearings 724 a, 723 b, and 724 b are roller bearings, andbearing 723 a is a ball bearing, though these bearing types may vary.The length L for shaft 722 is represented in some embodiments as thedistance between the midpoints or centers of the innermost bearings 724a, 723 b.

As yet another example, FIG. 7C conceptually shows a shaft 722 with aninbound duplex bearing configuration. Additional bearings located aroundthe circumference of the shaft 722 are omitted from FIG. 7C for clarity.According to some embodiments, a first pair of ball bearings 725 a, 726a is arranged in a duplex configuration aft of the mounting point 705 afor the booster 721. A second pair of ball bearings 725 b, 726 b isarranged in a duplex configuration forward of the mounting point 705 bfor the low-pressure turbine 720. Duplex bearing arrangements may alsobe referred to as double-row bearings, or overturning moment (OTM)bearings, since they provide moment stiffness to the shaft, i.e.,provide resistance to rotation across the bearing locations. In someembodiments duplex bearing types may include tandem bearings,back-to-back bearings, face-to-face bearings, and/or tapered rollerbearings.

In the example shown in FIG. 7C, both the first pair of ball bearings725 a, 726 a and the second pair of ball bearings 725 b, 726 b are in aninbound position, i.e., located closer towards the midshaft 727 than therespective mounting points 705 a, 705 b. In this position, the booster721 and the low-pressure turbine 720 are referred to as overhung. Thisinbound OTM layout is used in Embodiments 2, 4, and 6, for example,described above with reference to TABLES 1 and 2.

Alternatively, the first pair of ball bearings 725 a, 726 a and/or thesecond pair of ball bearings 725 b, 726 b may be in an outboundposition, as shown in FIG. 7D, i.e., located farther from the midshaft727 than the respective mounting points 705 a, 705 b of the booster 721and the low-pressure turbine 720. The length L for the duplex bearingconfigurations shown in FIG. 7C and FIG. 7D may be represented in someembodiments as the distance between the midpoints or centers of theinnermost ball bearings 726 a and 725 b, or alternatively, as thedistance between the center of the first pair of ball bearings 725 a,726 a and the center of the second pair of ball bearings 725 b, 726 b.The outbound OTM layout is used in Embodiments 3, 5, and 7, for example,described above with reference to TABLES 1 and 2.

As a further example, FIG. 7E conceptually shows a shaft 722 with atwo-bearing configuration. This configuration employs a first bearing724 a positioned aft of the mounting point 705 a for the booster 721,and a second bearing 724 b positioned aft of the mounting point 705 bfor the low-pressure turbine 720. The length L for this two-bearingconfiguration is represented in some embodiments as the distance betweenthe midpoints or centers of the bearings 724 a, 724 b. Alternativetwo-bearing configurations may position the two bearings in either anoutbound configuration or an inbound configuration. An example of atwo-bearing layout in an inbound configuration is shown in FIG. 1 , thatshows bearings 123 a, 123 b, 123 c, and 123 d are all located inbound ofthe mounting points for the booster 121 and the low-pressure turbine120. Note that in this context, two is the number of bearings along theshaft 722, and does not include additional bearings along thecircumference of the shaft 722. Embodiment 1, described above withreference to TABLE 1, uses a two-bearing layout in an outboundconfiguration (not shown).

In FIGS. 7A to 7E, the lines connecting the booster 721 to mountingpoint 705 a and low-pressure turbine 720 to mounting point 705 b areintended only to indicate schematically the general location of a netforce of the core engine components (e.g., booster 721 or low-pressureturbine 720) acting on the shaft 722 relative to the bearings, and isillustrated in this fashion only for purposes of illustrating arelationship between the nearest engine component relative to thebearing(s). It will be understood that the actual loading on a shaft isdistributed and comes from not only the engine components represented bybooster 721 and low-pressure turbine 720, but other nearby structures aswell. In these embodiments, the primary loading for purposes of thisdisclosure may, however, be thought of simply in terms of enginecomponents attached to the shaft 722 (e.g., low-pressure turbine 720 andbooster 721). It will be understood that the representation shown inFIGS. 7A to 7E is sufficient in defining the parts of the turbomachinethat mostly influence the shaft 722 behavior.

As discussed, at least one bearing may have an overturning moment (OTM)capability, which can resist relative rotation across the bearing in atleast a lateral plane or a vertical plane. These relative rotations mayoccur during bending of the shaft. The position along the shaft of suchbearings with OTM capabilities may directly affect the critical speed,by providing constraints to the relative rotations of the shaft, inaddition to the transverse support function of the bearings.

Examples of embodiments with different bearing arrangements aresummarized in TABLE 3. Generally, the inventors found that the number ofbearings, the position of the bearings and the OTM capability of thebearings can be selected to make a full range of operations subcriticalfor an engine. In other words, the selection of bearing layout canaffect (either increase or decrease) the shaft's critical speed.

TABLE 3 E/rho Teff Mode Embodiment L (in) D (in) Bearing type (in⁻¹)(in) (RPM) 8 60.6 2.75 4-bearing straddle 1.00E+08 0.35 7746 9 60.6 2.754-bearing straddle 1.00E+08 0.32 8555 10 60.6 2.75 4-bearing straddle1.27E+08 0.35 8832 11 82.2 2.74 4-bearing straddle 1.27E+08 0.32 9703 1260.6 2.75 inbound OTM 1.27E+08 0.32 11386 13 82.2 2.74 outbound OTM1.27E+08 0.32 7873

Embodiments 8, 9, 10, and 11 use a four-bearing straddle layout.Embodiments 8 and 9 use steel alloy, while Embodiments 10 and 11 usecomposite materials. Embodiments 8 and 10 have a uniform thicknessprofile, while Embodiments 9 and 11 have a concave thickness profile,manufactured using a bottle boring method. As a result of thesedifferences, the shaft mode critical speed occurs at 7746 RPM forEmbodiment 8, 8555 RPM for Embodiment 9, 8832 RPM for Embodiment 10, and9703 RPM for Embodiment 11.

Embodiments 11, 12, and 13 all use composite material and concavethickness profile via bottle boring. However, Embodiment 11 uses afour-bearing straddle layout, Embodiment 12 uses an inbound OTM bearinglayout, and Embodiment 13 uses an outbound OTM bearing layout. As aresult of these differences, the shaft mode critical speed occurs at9703 RPM for Embodiment 11, 11386 RPM for Embodiment 12, and 7873 RPMfor Embodiment 13.

Embodiment 11 can also be compared to Embodiments 8, 9, and 10 asdescribed with reference to TABLE 3. This allows a comparison of theimpact on critical speed of using composite material, variable thicknessprofile, and both, on a shaft with a four-bearing straddle layout.

Embodiment 12 can be compared to Embodiments 2, 4, and 6 described withreference to TABLE 2. This allows a comparison of the impact on criticalspeed of using composite material, variable thickness profile, and both,on a shaft with an inbound OTM layout.

Embodiment 13 can be compared to Embodiments 3, 5, and 7 described withreference to TABLE 2. This allows a comparison of the impact on criticalspeed of using composite material, variable thickness profile, and both,on a shaft with an outbound OTM layout.

Additionally, Embodiments 2 and 3 (in TABLE 1), and 10 (in TABLE 3) canbe compared, to evaluate the impact on critical speed of using differentbearing layouts on shafts using composite material. Embodiments 6 and 7(in TABLE 2) and 9 (in TABLE 3) can be compared, to evaluate the impacton critical speed of using different bearing layouts on shafts usingconcave thickness profiles.

The embodiments of turbomachine engines, and in particular the shaftsassociated with a power turbine described with reference to FIGS. 5A,5B, 6A to 6C, 7A, and 7B, were found to provide an improvement in theperformance of a shaft vis-à-vis its operating range. In addition to thementioned embodiments and those provided in TABLES 1 to 3, the types ofimprovements to the critical speed of the shaft when these features werecombined, taking into consideration the various benefits, as well asdown-sides, to selecting a particular configuration for a turbomachinearchitecture.

Examples of a subcritical shaft with a high redline speed include ashaft with a redline speed of, e.g., 70 ft/sec and adapted for a shaftmode of 5293 RPM, a shaft with a redline speed of, e.g., 75 ft/sec andadapted for a shaft mode of 6380 RPM, and a shaft with a redline speedof, e.g., 181 ft/sec and adapted for a shaft mode of 11410 RPM.

FIGS. 8A to 13 illustrate various gas turbine engines. In theembodiments of FIGS. 8A to 13 , the low-pressure shaft is supportedwithin the engine with different bearing arrangements. The gas turbineengines of FIGS. 8A to 13 may include structure that is the same as, orsimilar to, the gas turbine engines described with respect to FIGS. 1 to3 and the gas turbine engines may operate the same as, or similar, asthe turbine engines described with respect to FIGS. 1 to 3 .Accordingly, reference numerals are omitted from FIGS. 8A to 13 forclarity, but it is understood that features of similar appearance arethe same as or similar to the like features shown in FIGS. 1 to 3 .Although only one half of the gas turbine engine is shown in FIGS. 8A to13 , is its understood that a mirror image of the depicted half existson the other side of the centerline axis (e.g., similar to the gasturbine engine 100 shown in FIG. 1 ).

FIG. 8A shows a cross-sectional view of an exemplary gas turbine engine800 having a centerline axis 812. The gas turbine engine 800 includes alow-pressure compressor 821, a high-pressure compressor 818, alow-pressure turbine 820, and a high-pressure turbine 834. Thesefeatures operate in the same manner as described with respect to FIGS. 1to 3 . A low-pressure shaft 822 (also referred to as a “low-speedshaft”) extends between the low-pressure compressor 821 and thelow-pressure turbine 820. Together, the high-pressure compressor 818, acombustor (e.g., any of the combustors or combustion sections detailedherein), and the high-pressure turbine 834 define an engine core.

The low-pressure shaft 822 is rotationally supported in the gas turbineengine 800 with one or more bearings. In the embodiment illustrated inFIG. 8A, the gas turbine engine 800 includes a first bearing 823 a (alsoreferred to in the art as “Brg 2”), a second bearing 819 (also referredto in the art as “Brg 3”), a third bearing 825 (also referred to in theart as “Brg 4”), and a fourth bearing 823 b (also referred to in the artas “Brg 5”). The low-pressure shaft 822 is supported by one bearing on aforward side of the core engine (e.g., first bearing 823 a) and onebearing on an aft side of the core engine (e.g., fourth bearing 823 b).The high-pressure shaft is supported by the second bearing 819 on aforward side and the third bearing 825 on the aft side. The firstbearing 823 a and the second bearing 819 may be ball bearings, althoughother types of bearings or rotational supports are contemplated. Thethird bearing 825 and the fourth bearing 823 b may be roller bearings,although other types of bearings or rotational supports arecontemplated. Although shown as a single bearing at each location, thebearings may be a plurality of bearings. For example, the bearing 823 acould comprise two axially spaced bearings.

In FIG. 8A, the length LMSR is the length of the low-pressure shaft 822employed in relationship (1) (below) to determine the midshaft rating ofthe low-pressure shaft 822. The length LMSR is defined between theinboard low-pressure shaft forward bearing (e.g., the first bearing 823a) and the inboard low-pressure shaft aft bearing (e.g., the fourthbearing 823 b). The length LMSR is the lateral distance, parallel to thecenterline axis 812, defined between midpoints of the first bearing 823a and the fourth bearing 823 b.

The length LIGB is the length from the inboard low-pressure shaftforward bearing (e.g., the first bearing 823 a) to the core forwardbearing (e.g., the second bearing 819). The length L_(IGB) is thelateral distance, parallel to the centerline axis 812, defined betweenmidpoints of the first bearing 823 a and the second bearing 819.

The length L_(CORE) is the length of the engine core (e.g., the lengthincluding the high-pressure compressor 818, the combustor, and thehigh-pressure turbine 834). The length L_(CORE) is defined between thecore forward bearing (e.g., the second bearing 819) and the core aftbearing (e.g., the third bearing 825). The length L_(CORE) is thelateral distance, parallel to the centerline axis 812, defined betweenmidpoints of the second bearing 819 and the third bearing 825.

The length L_(AFT) is the length from aft of the core to the inboardlow-pressure shaft aft bearing (e.g., the fourth bearing 823 b). Thelength L_(AFT) is the lateral distance, parallel to the centerline axis812, defined between midpoints of the third bearing 825 and the fourthbearing 823 b.

The core diameter D_(CORE) represents the diameter of the engine core.The diameter D_(CORE) is defined by the outer diameter of the exit froma last stage 817 of the high-pressure compressor 818. The radius of thecore is shown in FIG. 8A as

$\frac{D_{CORE}}{2}.$

FIG. 8B shows a cross-sectional view of the exemplary gas turbine engineof FIG. 8A with the addition of a second forward bearing (e.g., anadditional bearing 815) on the low-pressure shaft 822. The additionalbearing 815 may be a roller bearing and the first bearing 823 a may be aball bearing. In this arrangement, the low-pressure shaft has twobearings forward of the core (e.g., first bearing 823 a and additionalbearing 815) and one bearing aft of the core (e.g., bearing 823 b).

FIG. 9 shows a cross-sectional view of an exemplary gas turbine engine900 having a centerline axis 912. The gas turbine engine 900 includes alow-pressure compressor 921, a high-pressure compressor 918, alow-pressure turbine 920, and a high-pressure turbine 934. Thesefeatures operate in the same manner as described with respect to FIGS. 1to 3 . A low-pressure shaft 922, (also referred to as a “low-speedshaft”), extends between the low-pressure compressor 921 and thelow-pressure turbine 920. Together, the high-pressure compressor 918, acombustor (e.g., any of the combustors or combustion sections detailedherein), and the high-pressure turbine 934 define an engine core.

The low-pressure shaft 922 is rotationally supported in the gas turbineengine 900 with one or more bearings. In the embodiment illustrated inFIG. 9 , the gas turbine engine 900 includes a first bearing 923 a (alsoreferred to in the art as “Brg 2”), a second bearing 919 (also referredto in the art as “Brg 3”), a third bearing 925 (also referred to in theart as “Brg 4”), a fourth bearing 923 b (also referred to in the art as“Brg 5”), and a fifth bearing 929 (also referred to in the art as “Brg6”). The low-pressure shaft 922 is supported by one bearing on theforward side of the core (e.g., first bearing 923 a) and two bearings onthe aft side of the core (e.g., fourth bearing 923 b and fifth bearing929). The high-pressure shaft is supported by the second bearing 919 ona forward side and the third bearing 925 on the aft side. The firstbearing 923 a and the second bearing 919 may be ball bearings, althoughother types of bearings or rotational supports are contemplated. Thethird bearing 925, the fourth bearing 923 b, and the fifth bearing 929may be roller bearings, although other types of bearings or rotationalsupports are contemplated.

In FIG. 9 , the length L_(MSR) is the length of the low-pressure shaft922 employed in relationship (1) (below) to determine the midshaftrating of the low-pressure shaft 922. The length L_(MSR) is definedbetween the inboard low-pressure shaft forward bearing (e.g., the firstbearing 923 a) and the inboard low-pressure shaft aft bearing (e.g., thefourth bearing 923 b). The length L_(MSR) is the lateral distance,parallel to the centerline axis 912, defined between midpoints of thefirst bearing 923 a and the fourth bearing 923 b.

The length L_(IGB) is the length from the inboard low-pressure shaftforward bearing (e.g., the first bearing 923 a) to the core forwardbearing (e.g., the second bearing 919). The length L_(IGB) is thelateral distance, parallel to the centerline axis 912, defined betweenmidpoints of the first bearing 923 a and the second bearing 919.

The length L_(CORE) is the length of the engine core (e.g., the lengthincluding the high-pressure compressor 918, the combustor, and thehigh-pressure turbine 934). The length L_(CORE) is defined between thecore forward bearing (e.g., the second bearing 919) and the core aftbearing (e.g., the third bearing 925). The length L_(CORE) is thelateral distance, parallel to the centerline axis 912, defined betweenmidpoints of the second bearing 919 and the third bearing 925.

The length L_(AFT) is the length from aft of the core to the inboardlow-pressure shaft aft bearing (e.g., the fourth bearing 923 b). Thelength L_(AFT) is the lateral distance, parallel to the centerline axis912, defined between midpoints of the third bearing 925 and the fourthbearing 923 b.

The length L_(AFT BRG) is the length from the inboard low-pressure shaftaft bearing (e.g., the fourth bearing 923 b) to an aftmost bearing(e.g., the fifth bearing 929). The length L_(AFT BRG) is the lateraldistance, parallel to the centerline axis 912, defined between midpointsof the fourth bearing 923 b and the fifth bearing 929.

The core diameter D_(CORE) represents the diameter of the engine core.The diameter D_(CORE) is defined by the outer diameter of the exit froma last stage 917 of the high-pressure compressor 918. The radius of thecore is shown in FIG. 9 as

$\frac{D_{CORE}}{2}.$

FIG. 10 shows a cross-sectional view of an exemplary gas turbine engine1000 having a centerline axis 1012. The gas turbine engine 1000 includesa low-pressure compressor 1021, a high-pressure compressor 1018, alow-pressure turbine 1020, and a high-pressure turbine 1034. Thesefeatures operate in the same manner as described with respect to FIGS. 1to 3 . A low-pressure shaft 1022, (also referred to as a “low-speedshaft”), extends between the low-pressure compressor 1021 and thelow-pressure turbine 1020. Together, the high-pressure compressor 1018,a combustor (e.g., any of the combustors or combustion sections detailedherein), and the high-pressure turbine 1034 define an engine core.

The low-pressure shaft 1022 is rotationally supported in the gas turbineengine 1000 with one or more bearings. In the embodiment illustrated inFIG. 10 , the gas turbine engine 1000 includes a first bearing 1023 a(also referred to in the art as “Brg 2”), a second bearing 1019 (alsoreferred to in the art as “Brg 3”), a third bearing 1025 (also referredto in the art as “Brg 4”), a fourth bearing 1023 b (also referred to inthe art as “Brg 5”), and a fifth bearing 1029 (also referred to in theart as “Brg 6”). The low-pressure shaft 1022 is supported by one bearingon the forward side of the core (e.g., first bearing 1023 a) and twobearings on the aft side of the core (e.g., fourth bearing 1023 b andfifth bearing 1029), where the two aft bearings are straddled as shownin FIG. 10 . The high-pressure shaft is supported by the second bearing1019 on a forward side and the third bearing 1025 on the aft side. Thefirst bearing 1023 a and the second bearing 1019 may be ball bearings,although other types of bearings or rotational supports arecontemplated. The third bearing 1025, the fourth bearing 1023 b, and thefifth bearing 1029 may be roller bearings, although other types ofbearings or rotational supports are contemplated.

In FIG. 10 , the length L_(MSR) is the length of the low-pressure shaft1022 employed in relationship (1) (below) to determine the midshaftrating of the low-pressure shaft 1022. The length L_(MSR) is definedbetween the inboard low-pressure shaft forward bearing (e.g., the firstbearing 1023 a) and the inboard low-pressure shaft aft bearing (e.g.,the fourth bearing 1023 b). The length L_(MSR) is the lateral distance,parallel to the centerline axis 1012, defined between midpoints of thefirst bearing 1023 a and the fourth bearing 1023 b.

The length L_(IGB) is the length from the inboard low-pressure shaftforward bearing (e.g., the first bearing 1023 a) to the core forwardbearing (e.g., the second bearing 1019). The length L_(IGB) is thelateral distance, parallel to the centerline axis 1012, defined betweenmidpoints of the first bearing 1023 a and the second bearing 1019.

The length L_(CORE) is the length of the engine core (e.g., the lengthincluding the high-pressure compressor 1018, the combustor, and thehigh-pressure turbine 1034). The length L_(CORE) is defined between thecore forward bearing (e.g., the second bearing 1019) and the core aftbearing (e.g., the third bearing 1025). The length L_(CORE) is thelateral distance, parallel to the centerline axis 1012, defined betweenmidpoints of the second bearing 1019 and the third bearing 1025.

The length L_(AFT) is the length from aft of the core to the inboardlow-pressure shaft aft bearing (e.g., the fourth bearing 1023 b). Thelength L_(AFT) is the lateral distance, parallel to the centerline axis1012, defined between midpoints of the third bearing 1025 and the fourthbearing 1023 b.

The length L_(AFT BRG) is the length from the inboard low-pressure shaftaft bearing (e.g., the fourth bearing 1023 b) to an aftmost bearing(e.g., the fifth bearing 1029). The length L_(AFT BRG) is the lateraldistance, parallel to the centerline axis 1012, defined betweenmidpoints of the fourth bearing 1023 b and the fifth bearing 1029.

The core diameter D_(CORE) represents the diameter of the engine core.The diameter D_(CORE) is defined by the outer diameter of the exit froma last stage 1017 of the high-pressure compressor 1018. The radius ofthe core is shown in FIG. 10 as

$\frac{D_{CORE}}{2}.$

FIG. 11 shows a schematic view of an exemplary gas turbine engine 1100having a centerline axis 1112. The gas turbine engine 1100 includes alow-pressure compressor or booster 1121, a high-pressure compressor1118, a low-pressure turbine 1120, and a high-pressure turbine 1134.These features operate in the same manner as described with respect toFIGS. 1 to 3 . In particular, the gas turbine engine 1100 is athree-stream, open fan engine, similar to the gas turbine engine of FIG.3 . A low-pressure shaft 1122, (also referred to as a “low-speedshaft”), extends between the low-pressure compressor 1121 and thelow-pressure turbine 1120. Together, the high-pressure compressor 1118,a combustor (e.g., any of the combustors or combustion sections detailedherein), and the high-pressure turbine 1134 define an engine core.

The low-pressure shaft 1122 is rotationally supported in the gas turbineengine 1100 with one or more bearings. In the embodiment illustrated inFIG. 10 , gas turbine engine 1100 includes a first bearing 1123 a (alsoreferred to in the art as “Brg 2”), a second bearing 1119 (also referredto in the art as “Brg 3”), a third bearing 1125 (also referred to in theart as “Brg 4”), a fourth bearing 1123 b (also referred to in the art as“Brg 5”), and a fifth bearing 1129 (also referred to in the art as “Brg6”). The low-pressure shaft 1122 is supported by two bearings on theforward side of the core (e.g., the first bearing 1123 a and a sixbearing 1115 forward of the first bearing 1123 a) and two bearings onthe aft side of the core (e.g., the fourth bearing 1123 b and the fifthbearing 1129). The high-pressure shaft is supported by the secondbearing 1119 on a forward side and the third bearing 1125 on the aftside. The first bearing 1123 a and the second bearing 1119 may be ballbearings, although other types of bearings or rotational supports arecontemplated. The third bearing 1125, the fourth bearing 1123 b, and thefifth bearing 1129 may be roller bearings, although other types ofbearings or rotational supports are contemplated.

In FIG. 11 , the length L_(MSR) is the length of the low-pressure shaft1122 employed in relationship (1) (below) to determine the midshaftrating of the low-pressure shaft 1122. The length L_(MSR) is definedbetween the inboard low-pressure shaft forward bearing (e.g., the firstbearing 1123 a) and the inboard low-pressure shaft aft bearing (e.g.,the fourth bearing 1123 b). The length L_(MSR) is the lateral distance,parallel to the centerline axis 1112, defined between midpoints of thefirst bearing 1123 a and the fourth bearing 1123 b.

The length L_(IGB) is the length from the inboard low-pressure shaftforward bearing (e.g., the first bearing 1123 a) to the core forwardbearing (e.g., the second bearing 1119). The length L_(IGB) is thelateral distance, parallel to the centerline axis 1112, defined betweenmidpoints of the first bearing 1123 a and the second bearing 1119. Thisspace is typically needed for the engine's accessory gearbox that iscoupled to the high-pressure (HP) shaft.

The term “IGB” refers to the inlet gearbox to drive the core to startthe engine, run pumps or other accessories. Referring to FIGS. 8A to 11, the location of the first bearing 823 a, 923 a, 1023 a, and 1123 arelative to the second bearing 819, 919, 1019, and 1119 may also bechosen for reasons isolating, or reducing a dynamic coupling betweenvibration modes of the LP shaft (i.e., bending mode excited between theLP shaft rotates at its critical speed) and modes associated with othercomponents supported by a separate frame from, or the same framesupporting the core. For example, referring to FIG. 11 , couplingbetween a modal property of the frame supporting the mid-fan (locateddirectly below the outlet guide vanes) and the modal property of the LPshaft may excite the LP shaft when the engine operates at certainspeeds. The distance L_(IGB) distance may also be affected when stagesare added or removed from the booster (e.g., booster 1121) and/or whenthe outlet guide vanes are moved closer or further away from the primaryfan. The L_(IGB) distance may also increase relative to the HPC frontend in order to align the forward bearing (e.g., first bearing 1123 a)more closely with the axial center of gravity of the frame supportingthe booster and OGV. The core is normally supported by a separate framefrom the frames that supports the fan, gearbox and booster. In someembodiments the first bearing 1123 a and the second bearing 1119 may belocated so as to provide direct support for both a center frame(supporting the core) and a forward frame (supporting, e.g., thebooster).

The length L_(CORE) is the length of the engine core (e.g., the lengthincluding the high-pressure compressor 1118, the combustor, and thehigh-pressure turbine 1134). The length L_(CORE) is defined between thecore forward bearing (e.g., the second bearing 1119) and the core aftbearing (e.g., the third bearing 1125). The length L_(CORE) is thelateral distance, parallel to the centerline axis 1112, defined betweenmidpoints of the second bearing 1119 and the third bearing 1125.

The length L_(AFT) is the length from aft of the core to the inboardlow-pressure shaft aft bearing (e.g., the fourth bearing 1123 b). Thelength L_(AFT) is the lateral distance, parallel to the centerline axis1112, defined between midpoints of the third bearing 1125 and the fourthbearing 1123 b. The length L_(AFT BRG) is the length from the inboardlow-pressure shaft aft bearing (e.g., the fourth bearing 1123 b) to anaftmost bearing (e.g., the fifth bearing 1129). The length L_(AFT BRG)is the lateral distance, parallel to the centerline axis 1112, definedbetween midpoints of the fourth bearing 1123 b and the fifth bearing1129. The bearing distances L_(AFT) and L_(AFT BRG) may be affected bythe number of stages in the LPT. If a stage is added then the distancesaftwards of L_(AFT) and/or L_(AFT BRG) from the HPT aft end may increasegiven the increased weight and support needed for additional stages,e.g., 3 to 4 stages, or 4 to 5 stages. Additionally, the bearings 1023b, 929 and 1123 b in the embodiments of FIGS. 9 to 11 may be desired forhigher speed LP shafts. The additional bearing can add a dampeningeffect to the LP shaft primary mode, or otherwise influence the modeshape so that its deflection at resonance is reduced. The bearingdistances L_(AFT) and L_(AFT BRG) may be affected by the presence of anelectric machine (e.g., the electric machine 390 described with respectto FIG. 3 ) coupled to the low-pressure shaft. The electric machine mayincrease the weight on the low-pressure shaft and, thus, increase theload that the bearings on the low-pressure shaft need to support and mayalso affect the frequency of the low-pressure shaft. Thus, the bearingdistances L_(AFT) and L_(AFT BRG) are affected by the additional loadfrom the electric machine. For example, in embodiments with an electricmachine near an aft portion of the core, the bearing distances mayincrease or decrease in a direction further aft or further forwardcompared to embodiments without an electric machine, depending on theparticular location of the electric machine within the engine. That is,the location of the bearings may be moved to a location more forward ormore aft as compared to embodiments without an electric machine.

The core diameter D_(CORE) represents the diameter of the engine core.The diameter D_(CORE) is defined by the outer diameter of the exit froma last stage 1117 of the high-pressure compressor 1118. The radius ofthe core is shown in FIG. 11 as

$\frac{D_{CORE}}{2}.$

FIG. 12 shows a partial cross-sectional view of an exemplary gas turbineengine 1200 having a centerline axis 1212. The gas turbine engine 1200includes a low-pressure compressor 1221, a high-pressure compressor1218, a low-pressure turbine 1220, and a high-pressure turbine 1234.Together, the high-pressure compressor 1218, a combustor (e.g., any ofthe combustors or combustion sections detailed herein), and thehigh-pressure turbine 1234 define an engine core. These features operatein the same manner as described with respect to FIGS. 1 to 3 . Alow-pressure shaft 1222, (also referred to as a “low-speed shaft”),extends between the low-pressure compressor 1221 and the low-pressureturbine 1220. A high-pressure shaft 1248 (also referred to as a“high-speed shaft”) is supported by bearings and connects thehigh-pressure compressor 1218 and the high-pressure turbine 1234. Asshown and previously described the high-pressure turbine 1234 includesone or more stages, represented by high-pressure turbine stage 1269.

FIG. 13 illustrates a cross-sectional detailed view 1350 of thehigh-pressure turbine stage 1269 of FIG. 12 . In the example of FIGS. 12and 13 , the high-pressure turbine 1234 has a core diameter D_(HPT BORE)defined by an inner diameter of the turbine stage 1269. The radius ofthe turbine stage 1269 is illustrated in FIG. 13 from the centerlineaxis 1212 to the high-pressure turbine stage 1269, and represented as

$\frac{D_{{HPT}{BORE}}}{2}.$The low-pressure shaft 1222 has a diameter D_(MSR) that is defined by anouter diameter of the low-pressure shaft 1222. The radius of thelow-pressure shaft 1222 is illustrated in FIG. 13 from the centerlineaxis 1212 to the outer diameter of the low-pressure shaft 1222, andrepresented as

$\frac{D_{MSR}}{2}.$The diameter D_(MSR) is the diameter employed in relationship (1) todetermine the midshaft rating of the low-pressure shaft 1222. Thedifference between D_(HPT CORE) and D_(MSR) define an intershaftthickness t.

As mentioned earlier, the inventors sought to improve upon the operatingspeed of a low-speed shaft, also referred to as the low-pressure shaft.With regard to the speed of the low-speed shaft, consideration was givennot simply to those factors affecting the low-pressure shaft, but alsoto factors considering the engine core of the engine, such as, thelength of the engine core, the diameter of the engine core, the materialof the components within the engine, the number of stages present in thehigh-pressure compressor, low-pressure compressor, high-pressureturbine, low-pressure turbine, and the location of bearings. In contrastto existing gas turbine engines requiring lower speeds, embodimentsconsidered presented challenges in determining how the low-speed shaftspeed could be increased without operating at or near a critical speed,for at least sustained periods of time or during standard flight periods(i.e., takeoff or max thrust).

Further, a selection of power turbine shaft and bearing arrangements,and location of those bearings for a turbomachine takes intoconsideration other factors, some of which can limit the selection of ashaft. The inventors however realized during the course of making theseveral embodiments referred to in the foregoing that there is aparticular range of designs, constraints on feasible designs thatprovided an unexpected benefit. The interplay between components canmake it particularly difficult to select or develop one component duringengine design and prototype testing, especially when some components areat different stages of completion. For example, one or more componentsmay be nearly complete, yet one or more other components may be in aninitial or preliminary phase where only one (or a few) design parametersare known. It is desired to arrive at what is possible at an early stageof design, so that the down selection of candidate optimal designs,given the tradeoffs, become more possible. Heretofore the process hassometimes been more ad hoc, selecting one design or another withoutknowing the impact when a concept is first taken into consideration.

Even taken separately from the integration of a shaft design with therest of an engine, modifying an existing shaft to increase its criticalspeed is challenging, and the impact of the different types ofimprovements and configurations on critical speed is not easilypredictable without empirical experimentation and simulation, which canbe enormously expensive and time-consuming. In some cases, amodification may even result in lowering the critical speed.

It is desirable to narrow the range of configurations or combination offeatures that can yield favorable results given the constraints of thedesign, feasibility, manufacturing, certification requirements, etc.early in the design selection process to avoid wasted time and effort.During the course of the evaluation of different embodiments as setforth above, the inventors discovered, unexpectedly, that there exists arelationship between the critical speed of the shaft and the ratio L/D(also referred to as LMSR/DMSR), which uniquely identifies a finite andreadily ascertainable (in view of this disclosure) number of embodimentssuitable for a particular architecture that can avoid a supercritical orcritical shaft situation during normal operation of an engine. Thisrelationship is referred to by the inventors as the midshaft rating(MSR), and is calculated according to the following relationship (1)between length, diameter and a redline speed (ft/sec) measured at theouter diameter of the shaft:Midshaft Rating MSR=(L _(MSR) /D _(MSR))(Shaft OD Speed atredline)^(1/2)  (1)

LMSR/DMSR is shaft length divided by effective shaft outer diameter. Theratio LMSR/DMSR is multiplied with the square root of the outer diameter(OD) rotation speed (OD Speed) at the redline speed for the enginearchitecture. Generally, the length LMSR and diameter DMSR are expressedin inches, and the shaft OD redline speed is the linear speed of theshaft surface. The OD redline speed in feet per second is calculated asthe shaft mode speed (in RPM) multiplied by the outer circumference ofthe shaft (the outer diameter of the shaft multiplied by the number π),and with additional corrections to convert from inches to feet and fromminutes to seconds. Accordingly, the midshaft rating has units of(velocity)½.

The midshaft rating identifies embodiments for a turbomachine's powerturbine that allow subcritical operation of the engine for a ratedredline speed. TABLE 5 lists embodiments of the turbine shaft along withits associated MSR value. The embodiments can inform one of thedimensions or qualities of the shaft that are believed reasonable andpractical for a shaft according to its basic features and the intended,rated critical speed. In other words, the midshaft rating, and,optionally, the LMSR/DMSR ratio and/or the OD speed at redline,indicates the operating ranges of interest, taking into account theconstraints within which a turbomachine operates, e.g., size,dimensions, cost, mission requirements, airframe type, etc.

In other embodiments, the midshaft rating may also, or alternatively, beused to define the propulsive system operating at a relatively highredline speed. Such things as the requirements of a propulsive system,the requirements of its subsystem(s), airframe integration needs andlimitations, and performance capabilities may, therefore, be summarizedor defined by the midshaft rating.

In still other embodiments, the midshaft rating may additionally providea particularly useful indication of the efficiency and effectiveness ofthe engine during initial development, e.g., as a tool to accept orreject a particular configuration. Thus, the midshaft rating can beused, for example, to guide low-speed shaft development. Therefore, themidshaft rating can also improve the process of developing aturbomachine engine.

As mentioned earlier, next generation gas turbine engine cores areexpected to operate at higher power densities, which can include a samelevel of power output as exists in current engines, but using a lighterweight core. A reduced weight core includes components coupled throughthe high speed shaft, which are the high-pressure compressor (HPC) andthe high-pressure turbine (HPT). A higher power density will also meanhigher engine operating temperatures, particularly at the HPC exitstage, combustor exit, HPT nozzle exit, and LPT. These changes in powerdensity also result in changes in core size (length, width, boreheights, etc.) and in some cases significant changes in core weight,such as when a CMC material is used for core components. As such, it isdesirable to assess the impact that next generation cores operating athigher power density can have on engine dynamics (e.g., dynamics of theLP shaft, the HP shaft, and/or a gearbox of the engine).

These changes in engine core size and weight effects not only thedynamic behavior of the HP shaft, but also can significantly influencethe dynamic behavior of the LP shaft, e.g., the critical speed, thatresults in undesired vibrations. Likewise, the dynamic behavior of theLP shaft can influence the dynamics of the HP shaft. Dynamic excitationof natural modes/frequencies of these two shafts, while decoupled inrotation from each other, nonetheless can interact and amplify eachother's natural modes of vibration via load paths through theirrespective supporting bearings.

The inventors sought to arrive at an engine architecture that hasacceptable dynamic behavior at redline, cruise and maximum thrustoperating conditions when a higher power density core is installed inthe engine, including whether the LP shaft can operate at a subcriticalspeed at redline when the higher power density core is used. Severalengine architectures were evaluated to determine whether changesreflecting a higher power density core would cause unacceptablevibration for either or both of the HP shaft and the LP shaft. The coreweights and sizes reflect improved performance from the generalperspective of a reduced Specific Fuel Consumption (SFC), but could alsocreate unanticipated or unmanageable dynamic excitation when the LPshaft and the HP shaft are operated at high speeds. It was necessarytherefore to study the impacts on MSR and related critical dynamics forvariations in such things as HPC stages to raise the overall pressureratio of the gas entering the combustion chamber, and/or an increasednumber of stages for the HPT, the overall length of the LP shaftaccounting for other changes in the engine cross-section affected bychanges in the HPC and/or HPT, and the impact on stiffness and weightwhen advanced material such as CMC material is used in the core.

Changes to these aspects of the core influence, not only an overalllength, weight, and size of the HPC and HPT, but also placement ofshaft-supporting bearings and accessories. Changes in the core affectplacement of other engine components encased within a core cowl. Thus,examining the effects of, e.g., adding an additional HPC stage, requirean understanding of adjacent engine components that need to accommodatean increased length of the core. To date, acceptable designs vs.unacceptable core design practice (from the perspective of structuraldynamics) have often involved an iterative process involving design onexperiment studies where many variations on architecture design areconsidered, with the hope that one of the variations might provide thedesired configuration satisfying both core performance and dynamicstability for both the HP shaft and LP shaft. After consideration ofseveral embodiments of a next generation engine core having between 8and 11 stages for an HPC and 1 to 2 stages for an HPT, as well asdifferent material (e.g., CMC material, Ni superalloys) each requiringdifferent bearing placements relative to the core, it was found thereare relationships between the length of the core, bearing supports ateach end and L_(MSR) for each of the foregoing modifications to a corethat produces a good approximation for the dynamic behavior of theengine. These relationships define the dynamic behaviors of the HP shaftand LP shaft in terms of factors attributable to a higher power densitycore, enabling the inventors to arrive at an improved engine design, onethat took into account the often competing interests between dynamicstability and achieving a more compact and higher power density core.

With reference back to FIGS. 8A to 11 , the LP shaft 822 length from theforward bearing 823 a to the aft bearing 823 b, i.e., L_(MSR), can bebroken down into three portions: a length forward of the core (L_(IGB)),a length aft of the core (L_(AFT)), and the portion of the LP shaft thatextends from the aft portion of the HPT to the forward end of the HPC(L_(CORE)). The flexural rigidity per unit length of the LP shaft alongthe length of the core is typically significantly lower than portionsoutside the core for embodiments disclosed herein of LP shaft where theflexural rigidity per unit length scales inversely with the shaft outerdiameter (e.g., same material throughout, no variation in wall thicknessthrough LP shaft across core, etc.).

L_(MSR) is defined according to the relationship:L _(MSR) =L _(IGB) +L _(CORE) +L _(AFT)  (2)

L_(IGB) represents a minimum distance from core forward end and forwardinboard low-pressure shaft bearing (e.g., 823 a in FIG. 8A) to theforward core bearing (e.g., 819 in FIG. 8A). The length L_(IGB) canrange from four inches to twelve inches (the minimum length of fourinches accommodates an accessary gearbox). The distance may be increasedor decreased depending on factors such as, location of other componentssupported by a common frame, the location of the axial center of gravityfor a frame, etc. as discussed earlier. Taking these factors intoconsideration, the length L_(IGB) may be estimated based on D_(CORE)using (3):L _(IGB)=0.16*D _(CORE)+1.7  (3)

Wherein D_(CORE) is the diameter (measured from the engine centerline)of the last stage of the high-pressure compressor, measured as the tipto tip diameter of the rotor of the exit or aft-most/last stage of thehigh-pressure compressor. D_(CORE) varies from ten inches to thirtyinches depending on whether there are 8, 9, 10 or 11 stages in the HPC.Examples are provided below in TABLE 4. Relation (3) is valid only foran HPC having 8, 9, 10 or 11 stages.

It was found, unexpectedly, after review and consideration of severaldifferent core sizes, that the following relationship exists between acore length L_(CORE), D_(CORE) and compressor and turbine stages.Relationship (4) provides a good approximation to the core length (e.g.,the length defined by the high-pressure compressor, the combustor, andthe high-pressure turbine). from the HPC entrance to HPT exit:

$\begin{matrix}{L_{CORE} = {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}}} & (4)\end{matrix}$

Thanks to this relationship, the influence of core length changesimpacted by adding additional HPC or HPT stages can be directly relatedto engine dynamics, thereby leading to in an improved engine design thatbalances dynamics needs against a higher pressure ratio core choice forhigher power density. The symbol m is the number of stages in thehigh-pressure compressor and n is the number of stages in thehigh-pressure turbine. The CIS accounts for changes in core supportingstructure, seals, nozzle sizes, and changes to the combustor lengthassociated with a change in the HPC and/or HPT stages. It was found thatCIS can be from twenty inches up to thirty inches for HPC stages rangingbetween 8 to 11 and 1 to 2 HPT stages. The relation in (4) for L_(CORE)is valid only for m being eight, nine, ten, or eleven, and n being oneor two.

The aft length L_(AFT) is the length from the aft core bearing (e.g.,third bearing 825 in FIG. 8A) to the aft inboard low-pressure shaftbearing (e.g., fourth bearing 823 b in FIG. 8A). It was found thatL_(AFT) can be from two inches to twenty-four inches, depending on thespecific spacing needs/preferences aft of the HPT and turbine rear frameintegration with the rotor. Also, placement of this bearing can beinfluenced by whether additional LPT stages are added, dynamics of theLP shaft and turbine rear frame. In some cases an additional bearingL_(AFT BRG) as discussed earlier

TABLE 4 shows various embodiments to determine LMSR according torelationships (2) to (4). The embodiments shown in TABLE 4 align withthe like embodiment numbers in FIGS. 20A to 20I.

TABLE 4 L_(MSR) L_(IGB) L_(CORE) L_(AFT) D_(CORE) CIS HPC HPT Embodimentin in in in in in stages stages 74 54.9 4 47 4 15 20 8 1 75 60.8 4 54 315 23 9 2 76 66.5 4 59 4 15 26 10 2 77 71.3 4 64 3 15 30 11 2 78 58.9 448 7 15 21 8 1 79 61.8 4 54 4 15 23 9 2 80 71.3 4 64 3 15 30 11 2 8160.4 4 52 4 17 22 8 1 82 64.9 4 58 3 17 23 9 2 83 68 6 58 4 16 24 10 284 75.9 4 69 3 17 30 11 2

D_(MSR) is defined according to the relationship:D _(MSR) =D _(HPT BORE)−2t  (5)

D_(HPT BORE) is the rotor bore diameter for the first stage of thehigh-pressure turbine. Its size may be approximated according to therelationship:D _(HPT BORE)=0.26D _(CORE)+0.6  (6)

The thickness t is the intershaft thickness between the low-pressureshaft and the high-pressure turbine bore (e.g., as shown in FIG. 13 ).The thickness t can vary from 450 mils and 650 mils (from 0.45 in to0.65 in).

CMC material is expected to be used in the HPT, LPT, and HPC parts of acore engine as this type of material can withstand higher temperaturesthan more traditional metal alloys. Given the differences in materialproperties for a CMC material, particularly the higher strength toweight ratio (or higher specific modulus) of CMC versus a metal alloyused in existing gas turbine engines in use currently, there is a needto ascertain the expected effects on HP shaft dynamics and LP shaftdynamics. Use of a CMC material introduces opportunities to increase acritical speed of the LP shaft, not only due to a weight reduction butalso in making more space available for increasing the LP shaft diameterextending through the core given the materials higher strength. Thecomponents made, at least in-part, from CMC material may include the HPcompressor rotors and disks, the HP turbine nozzles and/or rotors androtor disks, and the LP turbine nozzles and/or rotors and disks. CMCallows for components to be made more stiff or reduced in size whilehaving the same strength properties as metal alloys, thereby havingequivalent capability for sustaining high stresses associated withcentrifugal forces at high temperatures and operating speeds, inaddition to reducing the weight of the core, as compared to metals. CMCalso introduces new and untested structural dynamics, which canintroduce tradeoffs or compromise between a desired aero-performance(temperatures, rotation rates, pressure ratios) and stable dynamics atcruise, takeoff/max thrust and redline speeds for both the HP shaft andLP shaft.

CMC provided in the low-pressure turbine, which drives the LP shaft, canenable an increased critical speed due to a reduced weight, therebyaffecting MSR of the midshaft. For example, and referring back to FIGS.1 to 11 , rotors, blades, blades and discs, a single stage, or multiplestages (e.g., the turbine stages 266), in the low-pressure turbinemodule may be formed partially or wholly of CMC. In some embodiments, afirst, second, third, fourth or fifth stage of a LPT may have airfoilsmade from a CMC material, for example the aft-most stage airfoils (i.e.,3^(rd), 4^(th) or 5^(th) stage) may be made entirely or partially fromCMC material. LPT nozzles may be made from CMC material. Or both the LPTairfoils on rotor and nozzle airfoils may be made from CMC material.When CMC is used in the LPT, the inventors discovered that the criticalspeed at which the low-pressure shaft can operate is increasedsignificantly while also taking into account for the relatively brittlenature and temperature-dependent strength properties of CMC that goesalong with the reduced weight (or increase in specific strength)benefits that the material provides. That is, with strength andtoughness needs across different environments and operating conditionsrealized, the inventors found a relation between CMC material used inthe core for a resulting comparatively higher critical speed for the LPshaft, for maintaining a critical speed for increases in core lengthwhen used in the LPT, and for higher critical speeds without anassociated un-acceptable MSR value indicating that the design using CMCmaterial could have an LP shaft operating in a critical or supercriticalrange. In this way, the CMC material is used to increase the powerdensity of the gas turbine engine, while taking into account the affectson MSR and the engine dynamics. For example, and referring back to FIGS.1 to 14 , CMC used for the HPT and/or the HPC airfoils, HPT nozzle, androtor disks supporting airfoils that influence the length of the corecan influence the LP shaft design for other reasons as well, asexplained in greater detail below. Example embodiments showing effect onLP shaft MSR values and critical speed for CMC used in the LPT areincluded in the Tables of FIGS. 20A to 20I. It was found that for an LPTmade at least partially from CMC material the effective reduction inmass, i.e., the mass reduction can influence the MSR and critical speedby an amount that provides more opportunities for increased efficiencyby enabling a higher rotation speed. FIGS. 20A to 20I provide examples.

Use of CMC material in the HPT rotor blades also affects the size of theHPT bore radius, because the higher strength to weight ratio of CMCmaterial (when used for the rotor blades) reduces the strengthrequirements for the disk supporting the blades, thereby permitting thebore radius to increase. The bore radius limits the outer diameter ofthe LP shaft. It is desirable to increase the bore radius of thehigh-pressure turbine (first stage) to allow an increase in thelow-pressure shaft diameter (e.g., D_(MSR)). Referring to FIG. 14 , across-sectional view of a first stage HPT airfoil disk 1400 is shown.The blade disk 1400 has a bore radius r defined from an enginecenterline axis 1412 to an inner surface 1401 of the disk bore. Use ofCMC material for the rotor blade permits an increase in the radius r toenable a larger D_(MSR) for the LP shaft, thereby affecting the criticalspeed and MSR of the midshaft. CMC material for the bore disk may alsobe desired. Each blade disk 1400 has a width w measured from a forwardedge 1403 to an aft edge 1405. For a disk made from CMC material, theincreased specific modulus (strength/weight) may allow for a meaningfulreduction in the width w of the disk and therefore a reduction inL_(CORE), which can enable an increased critical speed and higher MSRvalue, which is desired. Even if a metal alloy is used for the disk, areduced width can be realized because of the lighter weight airfoil itneeds to support.

FIG. 15 compares the properties of MI and CVI type CMC material comparedto conventional metal alloys. The HPT may be made from CVI or MI typesof CMC material, or a hybrid of MI and CVI. In some embodiments the HPTis made from CVI type CMC material, such as the airfoil, while the diskis made from a metal alloy (separate parts coupled through a dovetailslot), or both the disk and airfoil is made from the CVI material(blisk). In some embodiments the surface of an airfoil (LPT, HPT eitheron nozzles or rotors) facing the hot gas may be made from CVI materialwhile the surface facing away from the hot gas is made from the MImaterial. The consideration of material to use includes not only hightemperature resistance but also the strength and toughness of thematerial.

Referring to FIG. 16 , the effects of using a CMC material in the HPTare shown. As more CMC material is used, the strength requirementsneeded to react the airfoil inertial loading reduces. As shown when theairfoil weight is reduced to 50% using CMC material, the radius of thebore increases by approximating 11%. This translates into a stiffer LPshaft (higher D_(MSR)), thereby providing a higher critical speed and ahigher MSR value. FIGS. 20A to 20I include embodiments of an enginewhere the MSR and/or critical speed may increase as a result of anincreased HPT disk bore radius.

Referring to FIG. 17 , further effects of using a CMC material in theHPT are shown. As more material is used, the strength requirementsneeded to react the airfoil inertial loading reduces. As shown when theairfoil weight is reduced to 50% using CMC material, the width of thebore decreases by approximately 17%. This translates into a stiffer HPand LP shaft (lower L_(CORE) and L_(MSR)), enabling higher criticalspeeds, mitigating against lower critical speeds as a result of addingadditional stages to the HPC and/or HPT. FIGS. 20A to 20I includeembodiments of an engine where the MSR and/or critical speed increasewhen the HPT disk width is decreased, enabling a decrease in L_(MSR).

In addition to the aforementioned dimensional and weight changes in thecore attributed to use of CMC material and affecting the LP shaftdynamics, using CMC material will also effect vibrational response forthe HP shaft, also referred to as HP shaft dynamics.

As alluded to earlier, the inventors further considered the effects thatan HP shaft has on LP shaft dynamics and how LP shaft dynamics can alsoinfluence HP shaft dynamics. Based on the studies done, it was foundunexpectedly that there are certain relationships between HP shaftdynamics and LP shaft dynamics that influence the design of a higherpower density core from the perspective of maintaining stable dynamicsduring engine operations. Referring to FIGS. 19A to 19C, there is showna schematic view of a high-pressure shaft (HP shaft) corresponding tothe predominate three typical mode shapes of the HP shaft that need tobe taken into consideration when designing an engine core and avoidingdynamic instability not only in the HP shaft, but also in the LP shaft,as realized by the inventors. The deformed HP shaft is supported at itsends by the HP shaft forward and aft bearings 1902 and 1904,respectively. The bearings are represented by their stiffnesses (shownas springs). FIG. 19A illustrates a first mode, also referred to as afundamental bounce mode, also known as a bow rotor mode, of thehigh-pressure shaft 1900. The first mode can occur at sub-idle speeds ofthe high-pressure shaft, which are about twenty percent to thirtypercent below a redline speeds of the low-pressure rotor (e.g., aboutten percent below cruise speeds). In FIG. 19B, the high-pressure shaft1900 has a second mode, also known as the pitch mode. The second modeoccurs at near to cruise speeds of the high-pressure shaft, which areabout twenty percent to thirty percent below the high-pressure shaftredline speeds. In FIG. 19C, the high-pressure shaft 1900 has a thirdmode, also known as a S-shaped mode. The third mode occurs near redlinespeeds of the high-pressure shaft.

The inventors found, during the course of evaluating several differentcore designs (designs that provide higher power densities, as discussedearlier) from the perspective of maintaining dynamic stability betweenand among the HP shaft and LP shaft the following relationships. Theserelationships take into account the trade-offs that need to be made, sothat the design accounts not only for features of the core length, sizeand weight, and representative of a higher overall pressure ratio andincreased operating temperatures (including use of CMC material), butalso the effects that these changes in the core can have on both the HPshaft and the LP shaft.

A first relationship concerns the high-pressure shaft redline speed, orhigh speed shaft rating HSR given by (7):

$\begin{matrix}{{HSR} = {10^{- 6}*N2_{r/l}*D_{CORE}*\left( \frac{L_{CORE}}{D_{CORE}} \right)^{2}}} & (7)\end{matrix}$

L_(CORE) and D_(CORE) are defined as described previously. N2_(r/l) isthe redline speed for the HP shaft. The redline speed N2_(r/l) is from11000 RPM to 25000 RPM. L_(CORE) is from forty-three inches to eightyinches. D_(CORE) is from 13.8 inches to 30.6 inches. HSR is from 1.9 to4.3.

For stable operating conditions the high-pressure shaft third modeshould be placed above the redline speed of the HP shaft and satisfying(8):−0.1822*HSR+HST>0  (8)

HST accounts for the effects that the HPC pressure ratio and the HPCexit temperature can have on the third mode. T25 is the temperature inRankine (R) at the high-pressure compressor (HPC) inlet. A goodapproximation for HST can be made in terms of only the T25, using (9):HST=−0.0014*T25+1.61  (9)

Where T25 is from 615 R to 855 R and HST is from 0.46 to 0.78.

For stable operating conditions the high-pressure shaft second modeshould be placed 20% below the redline speed of the HP shaft satisfying(10):

$\begin{matrix}{{{{- 0.1215}*{HSR}} + \left( \frac{{2*{HST}} - 1}{3} \right)} < {- 0.2}} & (10)\end{matrix}$

A second relationship concerns the low-pressure shaft redline speed, orhigh-speed shaft rating HSR_(LP) given by (11):

$\begin{matrix}{{HSR}_{LP} = {10^{- 6}*N1_{r/l}*D_{CORE}*\left( \frac{L_{CORE}}{D_{CORE}} \right)^{2}}} & (11)\end{matrix}$

L_(CORE) and D_(CORE) are defined as described previously. N1_(r/l) isthe redline speed for the LP shaft. For stable operating conditions thehigh-pressure shaft first mode should be placed either 20% below orabove the redline speed of the LP shaft satisfying (12):

$\begin{matrix}{{\frac{0.55}{\left( {HSR}_{LP} \right)^{2}} + {LST}} < {{{- 0.2}{OR}\frac{0.55}{\left( {HSR}_{LP} \right)^{2}}} + {LSR}} > 0} & (12)\end{matrix}$

LST accounts for the effects that the HPC pressure ratio and the HPCexit temperature can have on the first mode. T25 is the temperature inRankine (R) at the high-pressure compressor (HPC) inlet. A goodapproximation for LST can be made in terms of only the T25, using (13):LST=−0.0023*T25+1.18  (13)

Where T25 is from 615 R to 855 R and LST is from −0.2 to −0.74.

Relationships (7) through (13) when used together individually ortogether (depending on application or changes made to a design) canidentify an improved core accounting for characteristics associated witha higher power density (use of CMC material, increased number of HPCand/or HPT stages, increased bore height or length of the LP shaft) andbounding those features within constraints to avoid dynamic instabilityby interaction between one or more vibration modes of the LP shaft andHP shaft.

The foregoing indicates that employing CMC in the high-pressure turbineand/or the high-pressure compressor can benefit both the low-pressureshaft critical speed and the high-pressure shaft dynamics (e.g., thethird mode of the high-pressure shaft), or it can introduceunanticipated dynamic instability such as at a cruise condition. Asexplained earlier, CMC material used in the high-pressure turbine canprovide favorable reductions in disk width (e.g., FIG. 14 , width w) andincreased disk bore radius (e.g., FIG. 14 , radius r) which may bothreduce L_(MSR) and increase D_(MSR). The changes in core length can alsobenefit the third bending mode of the high-pressure shaft.

Additionally, CMC material used in high-pressure compressor(particularly the aft-most stages) can produce a noticeable increase inthe natural frequency of the HP shaft first and third mode because thislocation corresponds to the maximum deflection points for the first modeand the third mode (FIGS. 19A, 19C). Finally, as discussed earlier, CMCmaterial used for the HPT rotor blades (first stage) can result in awidth reduction of the HPT disk (e.g., FIG. 14 , width w), as well as anincreased bore radius for the HPT first stage disk bore (e.g., FIG. 14 ,radius r). These later changes to the HPT can improve the dynamics ofthe high-pressure shaft, including the third bending mode of thehigh-pressure shaft and the MSR because of the weight reduction andreduced L_(MSR) (reduces length of HP shaft correspondingly, therebymoving the third bending mode to a higher frequency), and D_(MSR)increase, respectively. Accordingly, the use of CMC material in the HPC,LPC, HPT, and/or the LPT provides for higher critical speeds and lowerweights, thereby increasing the MSR, and, thus, providing a higher powerdensity engine.

Furthermore, the inventors considered the effects that gearbox dynamicshave on LP shaft dynamics. Based on the studies done, it was foundunexpectedly that there are certain relationships between gearboxdynamics and LP shaft dynamics that influence the design of the couplingbetween the gearbox and the LP shaft. Embodiments taking into accountgearbox dynamics in combination with CMC are found in FIGS. 20A to 20I(e.g., embodiments 66 to 73, 85, and 86). FIG. 18 illustrates anenlarged, schematic side cross-sectional view of a gearbox assembly 1838with a mounting assembly 1800 for a gas turbine engine 1810, taken at acenterline axis 1812 of the gas turbine engine 1810. The gearboxassembly 1838 can be utilized as any of the gearbox assemblies and thegas turbine engine 1810 can be any of the gas turbine engines detailedherein. The gearbox assembly 1838 is substantially similar to thegearbox assembly 938 of FIGS. 9A and 9B and includes a planetaryconfiguration. For example, the gearbox assembly 1838 includes a sungear 1840, a plurality of planet gears 1842, a ring gear 1844, alow-speed shaft 1836 coupled to the sun gear 1840. The sun gear 1840 iscoupled via a flex coupling 1845 to the low-speed shaft 1836. Theplurality of planet gears 1842 are coupled together by a planet carrier1846. In the embodiment of FIG. 18 , the planet carrier 1846 is coupled,via a fan shaft 1848, to a fan (e.g., any of the fans or fan assembliesdetailed herein) to drive rotation of the fan about the centerline axis1812. The fan shaft 1848 is coupled to a fan frame 1849 via a fanbearing 1850. The ring gear 1844 is coupled via a flex mount 1847 to anengine static structure 1819. The flex coupling 1845, the flex mount1847, and the fan frame 1849 define the mounting assembly 1800 for thegearbox assembly 1838. As described herein, the flex coupling 1845, theflex mount 1847, and the fan frame 1849 may be referred to as mountingmembers.

In FIG. 18 , the flex coupling 1845 is part of an input shaft 1851 thatextends from a forward bearing 1852 of the low-speed shaft 1836 to thesun gear 1840 (e.g., to an axially center of the sun gear 1840). Theflex coupling 1845 is also referred to as a decoupler, and includes oneor more flex plates 1854 that absorb and reduce deflections andvibrations from propagating from the gearbox assembly 1838 to thelow-speed shaft 1836 or from the low-speed shaft 1836 to the gearboxassembly 1838. In the embodiment shown in FIG. 18 , the one or more flexplates 1854 include a first flex plate 1854 a and a second flex plate1854 b spaced axially from each other along the input. The one or moreflex plates 1854 can include any number of flex plates located at anyaxial position along the input, as desired. The flex plates 1854 areintegral with the flex coupling 1845 and include axial gaps that absorbthe deflections in an axial direction so that propagation of thedeflections through the flex coupling 1845 is reduced. Accordingly, theflex coupling 1845 can be tuned or can be changed to achieve aparticular desired vibrational frequency response such that vibrationsof the gearbox assembly 1838 do not excite the low-speed shaft 1836 whenthe redline speed is subcritical.

The input shaft 1851 includes an input shaft length L_(input) thatextends axially from the forward bearing 1852 to the sun gear 1840(e.g., an axial center of the sun gear 1840). The input shaft lengthL_(input) is equal to an aft decoupler length L_(dplr_aft), a decouplerlength L_(dcplr), and a forward decoupler length L_(dcplr_fwd), addedtogether. The aft decoupler length L_(dplr_aft) extends from the forwardbearing 1852 to the first flex plate 1854 a, the decoupler lengthL_(dcplr) extends from the first flex plate 1854 a to the second flexplate 1854 b, and the forward flex length L_(dcplr_fwd) extends from thesecond flex plate 1854 b to the sun gear 1840 (e.g., to an axiallycenter of the sun gear 1840). The flex coupling 1845 also includes adecoupler height H_(dcplr) and one or more decoupler radii. Thedecoupler height is a height of the flex plates 1854 in the radialdirection from the input shaft 1851. The one or more decoupler radii isan inner radius of the input shaft 1851. The one or more decoupler radiiinclude a first decoupler radius R_(dcplr1) and a second decouplerradius R_(dcplr2). In the embodiment of FIG. 18 , the first decouplerradius R_(dcplr1) is equal to the second decoupler radius R_(dcplr2)such that the input shaft 1851 has a constant inner radius. In someembodiments the first decoupler radius R_(dcplr1) is different than thesecond decoupler radius R_(dcplr2) such that the input shaft 1851 has avariable inner radius (e.g., the inner radius of the input shaft 1851changes along the axial direction).

In consideration of midshaft operating speeds, whether during anaircraft maximum thrust at takeoff, redline or cruise operatingcondition, it is desirable to have any anticipated dynamic loading ofthe gearbox caused by midshaft motion to not act as to amplify or excitefundamental or principle mode(s) of the gearbox through the sungear—midshaft coupling. It is also desirable to avoid a dynamicexcitation communicated through the sun gear/midshaft coupling andinfluenced by modal characteristics of the gearbox assembly to act as toexcite fundamental mode(s) of the midshaft. To achieve this end result,it is desirable to have a decoupler moment stiffness KM_(dcplr) of theflex coupling 1845 and a decoupler shear stiffness KS_(dcplr) of theflex coupling 1845 (e.g., a moment stiffness and a shear stiffness atthe sun gear-midshaft coupling) being such as to neither causesignificant excitation of a fundamental midshaft mode, nor a dynamicexcitation from the midshaft communicated at this coupling to causesignificant excitation of a fundamental mode of the gearbox assembly.The decoupler moment stiffness KM_(dcplr) is an overturning momentstiffness of the flex coupling 1845 (e.g., a torque of the flex coupling1845 applied radially on the flex coupling 1845), including thedecoupler moment stiffness of the first flex plate 1854 a and thedecoupler moment stiffness of the second flex plate 1854 b. Thedecoupler shear stiffness KS_(dcplr) is a stiffness of the flex coupling1845 (e.g., between the first flex plate 1854 a and the second flexplate 1854 b) in the axial direction. The stiffness of the flex coupling1845 (e.g., the decoupler moment stiffness KM_(dcplr) and the decouplershear stiffness KS_(dcplr)) should be selected so as to not amplifymidshaft properties or so as not excite the gearbox assembly 1838 bymidshaft dynamic behavior during engine operation.

Various rig tests and measurements taken to simulate engine operationalconditions, accounting for any differences between a dynamic responsefor a recently fielded engine and an engine after several operationalcycles, revealed common patterns in dynamic behavior formidshaft-gearbox interactions to inform the design of the flex coupling1845 to avoid the modal coupling between gearbox and midshaft explainedabove. It was found that a decoupler moment stiffness KM_(dcplr) of theflex coupling 1845 in a range of 50 klb*in/rad to 200 klb*in/rad, and adecoupler shear stiffness KS_(dcplr) of the flex coupling 1845 in arange of 100 klb/in to 500 klb/in, should substantially avoidintolerable or sustained dynamic amplification of the gearbox assembly1838 or the midshaft (e.g., the low-speed shaft) when there isexcitation of either the gearbox assembly 1838 or the midshaft duringengine operations. In this way, the flex coupling 1845 prevents thegearbox assembly 1838 from dynamically exciting the midshaft, andprevents the midshaft from dynamically exciting the gearbox assembly1838. In this way, the gearbox and its couplings are designed to preventthe gearbox dynamics from affecting the midshaft dynamics at subcriticalspeeds of the LP shaft, and vice versa. The decoupler moment stiffnessKM_(dcplr) of the flex coupling 1845 is expressed in klb*in/rad, and thedecoupler shear stiffness KS_(dcplr) of the flex coupling 1845 isexpressed in klb/in. In view of the foregoing, the decoupler momentstiffness KM_(dcplr) of the flex coupling 1845 and the decoupler shearstiffness KS_(dcplr) of the flex coupling 1845 are desired to satisfythe relationships (14) and (15), respectively:

$\begin{matrix}{{KM}_{dcplr} = \frac{E*K_{m}*R_{dcplr}^{4}}{H_{dcplr}}} & (14)\end{matrix}$ $\begin{matrix}{{KS}_{dcplr} = \frac{E*K_{s}*R_{dcplr}^{4}}{L_{dcplr}^{2}}} & (15)\end{matrix}$

TABLE 5 lists the bearing layout, the strength-to-weight ratio E/rho ininches⁻¹, the effective thickness T_(eff) in inches, the critical speedcorresponding to the shaft's fundamental mode in RPM, the OD linearspeed at redline in ft/sec, the length-to-diameter ratio L_(MSR)/D_(MSR)(dimensionless), and MSR in (ft/sec)^(1/2) for all the embodiments (1 to13) of Tables 1 to 3, as well as a number of additional embodiments (14to 32). As noted above, L_(MSR)/D_(MSR) represents the ratio of thelength over the outer diameter of the low-pressure/low-speed shaft. Whenthe shaft has a variable diameter over its length, the outer diametermay be the diameter at the midshaft. E/rho represents the materialcomposition of the shaft, and T_(eff) represents an effective wallthickness of the shaft. For shafts with variable thickness over theirlength, the wall thickness may be the thickness at the midshaft.

TABLE 5 L_(MSR)/ Redline E/rho T_(eff) Mode D_(MSR) OD Speed MSREmbodiment Bearing Layout in⁻¹ in RPM in/in ft/sec (ft/sec)^(1/2) 12-bearing outbound 1.00E+8 0.35 4181 30 50 214 2 inbound OTM 1.27E+80.35 10263 22 123 247 3 outbound OTM 1.27E+8 0.35 6915 30 83 275 4inbound OTM 1.00E+8 0.35 9001 22 108 231 5 outbound OTM 1.00E+8 0.356065 30 73 257 6 inbound OTM 1.00E+8 0.32 10039 22 121 242 7 outboundOTM 1.00E+8 0.32 6942 30 83 272 8 4-bearing straddle 1.00E+8 0.35 774622 93 214 9 4-bearing straddle 1.00E+8 0.32 8555 22 103 223 10 4-bearingstraddle 1.27E+8 0.35 8832 22 106 229 11 4-bearing straddle 1.27E+8 0.329703 30 116 322 12 inbound OTM 1.27E+8 0.32 11386 22 137 257 13 outboundOTM 1.27E+8 0.32 7873 30 94 290 14 4-bearing outbound 1.00E+8 0.35 626226 72 219 15 2-bearing aft 1.27E+8 0.29 8255 21 109 215 16 2-bearing aft1.27E+8 0.31 13323 14 233 216 17 2-bearing aft 1.27E+8 0.47 5667 23 83210 18 2-bearing aft 1.27E+8 0.29 6380 24 83 215 19 2-bearing aft1.27E+8 0.31 9821 17 154 216 20 2-bearing aft 1.27E+8 0.47 4586 26 67211 21 2-bearing aft 1.00E+8 0.23 6380 24 84 217 22 2-bearing aft1.00E+8 0.25 13493 14 235 218 23 2-bearing aft 1.00E+8 0.38 4586 27 62210 24 2-bearing aft 1.27E+8 0.29 6619 25 87 231 25 2-bearing aft1.27E+8 0.31 11065 17 176 232 26 2-bearing aft 1.27E+8 0.47 4852 28 64224 27 4-bearing straddle 1.00E+8 0.29 6380 28 75 245 28 inbound OTM1.00E+8 0.31 10666 19 165 247 29 outbound OTM 1.00E+8 0.47 4586 31 59239 30 4-bearing straddle 1.27E+8 0.23 6380 35 70 289 31 inbound OTM1.27E+8 0.25 11410 22 181 294 32 outbound OTM 1.27E+8 0.38 5293 33 70276

Embodiments 15 to 26 use a two-bearing aft layout. These embodimentsdiffer in using composite materials, different shaft geometries, andvariable thickness profiles.

Embodiments 15 to 17 use a composite material instead of steel alloy.These embodiments differ in shaft geometry, with differentL_(MSR)/D_(MSR) ratios ranging from 14 to 23.

Embodiments 18 to 20 use a composite material instead of a steel alloy.These embodiments also differ from each other in shaft geometry (e.g.,L_(MSR)/D_(MSR) ratio). These also differ from Embodiments 15 to 17, inbeing longer and thinner, resulting in a higher range of L_(MSR)/D_(MSR)ratio, from 17 to 26.

Embodiments 21 to 23 use a steel alloy, vary the shaft geometry (lengthand/or diameter), and have a concave thickness profile. These differfrom each other in terms of their effective thickness. These embodimentsmay be compared to Embodiments 24 to 26, which use composite materials,vary the shaft geometry (length and/or diameter), and have a concavethickness profile.

Embodiments 27 to 32 use different bearing layouts. Embodiments 27 to 29use steel alloy and have varying geometry. Embodiments 30 to 32 usecomposite material and a concave thickness profile, in addition tovarying geometry.

FIGS. 20A to 20I, illustrate additional embodiments 33 to 86 taking intoaccount the effects of the change in core dimensions (e.g., stages,lengths, diameters, etc.) and use of CMC described previously. Thecomparisons described below are in relation to the embodiments 1 to 32described in TABLE 5.

Embodiments 33 to 36 use CMC for various components in the low-pressureturbine to help reduce the weight. These embodiments differ from eachother in terms of bearing arrangements, and maintain the same stiffnessas comparable embodiments 1, 2, and 8 (described above in TABLE %)without CMC components. The use of CMC provides a reduced overhungweight, which has the effect of increasing the allowable OD speed atredline and/or enabling a higher MSR.

Embodiments 37 to 40 use CMC for various components in both thelow-pressure turbine and the core (e.g., the high-pressure turbine). Theuse of CMC in the low-pressure turbine reduces the weight. The use ofCMC in the core increases the bore radius of the core, thus allowing foran increase in diameter of the low-pressure shaft. That is, embodiments37 to 40, have a larger radius for the low-speed shaft (3 inches)relative to embodiments without CMC in the core, for example,embodiments 1, 2, 8, and 33 to 36, which employ CMC only in the LPT(having a low-speed shaft diameter of 2.7 inches). Embodiment 39 furtherincludes the addition of using bottle boring for a variable low-speedshaft thickness. The increased bore radius generally provides a lowerL_(MSR)/D_(MSR) ratio (see for example, a comparison with embodiments 1,2, 8, and 33 to 36) and/or enabling an increased MSR.

Embodiments 41 to 45 use different combinations of bottle boring and CMCfor various components in both the LPT and the HPT. These embodimentshave an even larger radius (4 inches) for the low-speed shaft, as wellas a lower effective thickness (see, for example, a comparison withembodiments 1, 4, 8, and 37 to 40) generally resulting in a higherredline speeds and/or higher MSR. Embodiments 43 and 44 furtherincluding bottle boring. Embodiment 44 includes a 2+1 bearing systemarrangement, such as described with respect to FIG. 8B.

Embodiments 46 to 51 use different combinations of bottle boring and CMCfor various components in both the LPT and the HPT. These embodimentshave an even larger radius (4 inches) for the low-speed shaft, as wellas a lower effective thickness (see, for example, a comparison withembodiments 1, 4, 8, and 37 to 40). Embodiments 46 to 51 further includea composite material shaft. Embodiments 46 to 51 include CMC in the HPTa manner that increases the bore radius (e.g., as described with respectto FIG. 14 ). Embodiment 48 further includes CMC in the HPT in a mannerthat decreases the core length (e.g., as described with respect to FIG.14 ). This results in increased strength to weight ratio (1.3E+8 in).The combination of CMC in the LPT, CMC in the HPT, and a compositematerial shaft facilitates higher redline speeds and/or higher MSR.

Embodiment 52 used a three-bearing system, including bottling boring.Embodiments 53 to 59 begin with this as a baseline and adjust variousfactors. Each additional embodiment from embodiments 53 to 59 builds onthe prior embodiment. Embodiment 53 adds CMC in the LPT to embodiment52. Embodiment 54 adds CMC in another stage of the LPT to embodiment 53.Embodiment 55 includes a composite material in the low-speed shaft addedto the embodiment 54. Embodiment 56 adds the core increase benefits ofCMC in the HPT to embodiment 55. Embodiment 57 is based on embodiment 56but with a 9 stage core. Embodiment 58 is based on embodiment 57, butwith two bearings in the forward position and one bearing in the aftposition on the LPT (e.g., the arrangement described with respect toFIG. 8B). Embodiment 59 adds another core stage to embodiment 58. Thesevariations resulted in increased redline speed and/or higher MSR.

Embodiment 60 used a three-bearing system, including bottling boring.Embodiments 61 to 65 begin with this as a baseline and adjust variousfactors. Each additional embodiment from embodiments 61 to 65 builds onthe prior embodiment. Embodiment 61 adds CMC in the LPT to embodiment60. Embodiment 62 includes a composite material in the low-speed shaftadded to the embodiment 61. Embodiment 63 adds the core increasebenefits of CMC in the HPT to embodiment 62. Embodiment 64 is based onembodiment 63 but with a 9 stage core. Embodiment 65 is based onembodiment 64, but with two bearings in the forward position and onebearing in the aft position on the LPT (e.g., the arrangement describedwith respect to FIG. 8B). These variations resulted in increased redlinespeed and/or higher MSR.

Embodiments 66 to 69 all use CMC in the LPT and CMC in the HPT to takeadvantage of the core increase benefits. Embodiments 66 and 67 use afour-bearing system and include bottle boring. Embodiments 68 and 69include a two-bearing system having a forward inbound bearing and an aftoutbound bearing and include bottle boring. The embodiments of 66 to 69further have differences in terms of stiffness (e.g., decoupler shearstiffness and/or decoupler moment stiffness). As shown, embodiments 67and 69 achieve a greater shear stiffness than embodiments 66 and 68,respectively, generally resulting in substantially higher redline speedsand/or higher MSR.

Embodiments 70 to 73 all use CMC in the LPT and CMC in the HPT to takeadvantage of the core increase benefits. Embodiments 70 and 71 use afour-bearing system and include bottle boring. Embodiments 72 and 73include a two-bearing system having a forward inbound bearing and an aftoutbound bearing and include bottle boring. The embodiments of 70 to 73further have differences in terms of stiffness (e.g., decoupler shearstiffness). As shown, embodiments 71 and 73 achieve a greater shearstiffness than embodiments 70 and 72, respectively, generally resultingin substantially higher redline speeds and/or higher MSR. Embodiments 70to 73 differ from embodiments 66 to 69 in that the embodiments have asmaller LP shaft diameter.

In each of the embodiments 74 to 84, L_(MSR) is determined based on therelationship (2) described previously. In embodiments 74 to 77 CMC isnot used. In embodiments 78 to 84, CMC is used in the LPT and the HPT.In embodiments 78 to 80, the CMC is used in the HPT to increase the coreradius. In the embodiments 81 to 84 the CMC is used in the HPT todecrease the core length and increase the core radius. As shown inembodiments 74 to 84, this allows increase in redline speeds and/or MSR.

Embodiments 85 and 86 both use CMC in the LPT and CMC in the HPT to takeadvantage of the core increase benefits. Embodiments 85 and 86 bothinclude a two-bearing system having a forward inbound bearing and an aftoutbound bearing and include bottle boring. The embodiments differ interms of stiffness (e.g., decoupler shear stiffness and/or decouplermoment stiffness). As shown, embodiment 86 achieves a greater shearstiffness and greater moment stiffness than embodiment 85, generallyresulting in a substantially higher redline speed and/or higher MSR.

Based on the experimentation described above, the inventors identifiedembodiments with MSR between two hundred and three thirty hundred(ft/sec)⁻¹ and OD redline speeds ranging from fifty to two hundred sixtyft/sec and with L_(MSR)/D_(MSR) ratio ranging from twelve tothirty-seven were possible and indicated noticeable improvements insubcritical range when the power turbine shaft incorporates the variousaspects of the disclosure.

TABLE 6 summarizes examples of different operating ranges forembodiments, such as the embodiments listed in TABLE 5. For example, anembodiment can be configured with a L_(MSR)/D_(MSR) ranging betweentwelve and twenty may have an OD speed between one hundred and fifty andtwo hundred and fifty ft/sec, and a corresponding range of MSR betweenone hundred ninety and two hundred forty-five (ft/sec)^(1/2). As anotherexample, an embodiment can be configured with a L_(MSR)/D_(MSR) rangingbetween sixteen and thirty may have an OD speed between seventy-five andone hundred seventy-five ft/sec, and a corresponding range of MSRbetween two hundred twelve and two hundred sixty (ft/sec)^(1/2). Asstill another example, an embodiment can be configured with aL_(MSR)/D_(MSR) ranging between twenty-six and thirty-seven may have anOD speed between sixty and ninety ft/sec, and a corresponding range ofMSR between two hundred forty-seven and two hundred eighty-sevenft/sec)^(1/2). These low, nominal, and high ranges as summarized inTABLE 6 are general examples, and individual embodiments may exceedthese values.

TABLE 6 L_(MSR)/ Redline OD Example Limits D_(MSR) Speed MSR and Ranges(in/in) (ft/sec) (ft/sec)^(1/2) Low limit 12 250 190 20 150 245 Nominallimit 16 175 212 30 75 260 High Limit 26 90 247 37 60 287

According to additional embodiments, CMCs were evaluated in thelow-pressure turbine and high-pressure turbine, in combination withdifferent bearing configurations, different effective shaft thicknesses,different shaft diameters, different shaft materials (e.g., composites),and a variety of combinations thereof, in order to determine whichcombinations would work best for a given architecture and need, as wellas taking the competing engineering requirements into account. Some ofthese embodiments are summarized in FIGS. 20A to 20I.

FIGS. 20A to 20I list the bearing layout, the strength-to-weight ratioE/rho in inches⁻¹, the effective thickness T_(eff) in inches, thecritical speed corresponding to the shaft's fundamental mode in RPM, theOD linear speed at redline in ft/sec, the length-to-diameter ratioL_(MSR)/D_(MSR) (dimensionless), and MSR in (ft/sec)^(1/2) for a numberof additional embodiments (33 to 59). As noted above, L_(MSR)/D_(MSR)represents the ratio of the length over the outer diameter. When theshaft has a variable diameter over its length, the outer diameter may bethe diameter at the midshaft. E/rho represents the material compositionof the shaft, and T_(eff) represents an effective wall thickness of theshaft. For shafts with variable thickness over their length, the wallthickness may be the thickness at the midshaft.

FIG. 21A illustrates acceptable ranges for LP shaft redline speeds for aMSR region 2115, ranging from 200 (ft/sec)⁻¹ (curve 2120) to 300(ft/sec)⁻¹ (curve 2125), for redline speeds from fifty to two hundredand fifty feet per second and shafts having an L_(MSR)/D_(MSR) fromtwelve to forty three.

FIG. 21B illustrates acceptable ranges for LP shaft redline speeds for aMSR region 2130, ranging from 200 (ft/sec)⁻¹ (curve 2135) to 300(ft/sec)⁻¹ (curve 2140), for L_(MSR)/D_(MSR) ratios from twelve tothirty-seven and redline speeds from thirty to six hundred thirty feetper second.

FIG. 21C illustrates acceptable ranges for LP shaft redline speeds for aMSR region 2145, ranging from one hundred ninety (ft/sec)⁻¹ (curve 2150)to three hundred thirty (ft/sec)⁻¹ (curve 2155), for L_(MSR)/D_(MSR)between twelve and thirty seven. Examples are provided in TABLE 5 andFIGS. 20A to 20I. FIG. 21C shows an MSR ranging from one hundred ninety(ft/sec)⁻¹ (curve 2150) to three hundred thirty (ft/sec)⁻¹ (curve 2155),for L_(MSR)/D_(MSR) ratios from twelve to thirty-seven and redlinespeeds from fifty to two hundred and sixty feet per second.

In view of the foregoing objectives, in at least certain embodiments, apropulsion system is configured to define an MSR greater than onehundred ninety (ft/sec)^(1/2), such as greater than two hundred(ft/sec)^(1/2), such as at least two hundred thirty-five (ft/sec)^(1/2),up to at least three hundred thirty (ft/sec)^(1/2).

In view of the foregoing objectives, in at least certain embodiments, apropulsion system is configured to define an L_(MSR)/D_(MSR) ratiogreater than twelve, such as greater than sixteen, such as at leasttwenty-six, up to at least thirty-seven.

In view of the foregoing objectives, in at least certain embodiments, apropulsion system is configured to define an OD redline speed greaterthan sixty ft/sec, such as greater than seventy five ft/sec, such as atleast one hundred and fifty ft/sec, up to at least two hundred and sixtyft/sec.

Based on the teachings in this disclosure, and without limiting thedisclosure to only those embodiments explicitly shown, it will beunderstood how both the manner and the degree to which a modification ofshaft length, diameter, material composition, bearings configuration,and thickness profile affects the MSR, and, additionally, the competingrequirements, or requirements for a turbomachine architecture (e.g.,available spacing/packaging, clearance, sump location, lubrication,etc.) for a given MSR.

Further aspects of the present disclosure are provided by the subjectmatter of the following clauses.

A turbomachine engine includes a core engine having one or morecompressor sections, one or more turbine sections that includes a powerturbine, and a combustion chamber in flow communication with thecompressor sections and turbine sections. The turbomachine engine alsoincludes a shaft that is coupled to the power turbine and that ischaracterized by a midshaft rating (MSR) between two hundred(ft/sec)^(1/2) and three hundred (ft/sec)^(1/2), and a redline speedbetween fifty and two hundred fifty feet per second (ft/sec).

A turbomachine engine includes a core engine having one or morecompressor sections, one or more turbine sections that includes a powerturbine, and a combustion chamber in flow communication with thecompressor sections and turbine sections. The turbomachine engine alsoincludes a shaft that is coupled to the power turbine and that ischaracterized by a midshaft rating (MSR) between two hundred(ft/sec)^(1/2) and three hundred (ft/sec)^(1/2), a length L_(MSR), anouter diameter D_(MSR), and a ratio of L_(MSR)/D_(MSR) between twelveand thirty-seven.

The turbomachine engine of any preceding clause, wherein theturbomachine engine is configured to operate up to a redline speedwithout passing through a critical speed associated with a first-orderbending mode of the shaft.

The turbomachine engine of any preceding clause, wherein theturbomachine engine is configured to operate up to the redline speedwithout passing through a critical speed associated with a first-orderbending mode of the shaft.

The turbomachine engine of any preceding clause, wherein the MSR isbetween one hundred ninety (ft/sec)^(1/2) and two hundred forty-five(ft/sec)^(1/2).

The turbomachine engine of any preceding clause, wherein the MSR isbetween two hundred twelve (ft/sec)^(1/2) and two hundred sixty(ft/sec)^(1/2).

The turbomachine engine of any preceding clause, wherein the MSR isbetween two hundred forty-seven (ft/sec)^(1/2) and two hundred ninety(ft/sec)^(1/2).

The turbomachine engine of any preceding clause, wherein the redlinespeed is between sixty and ninety ft/sec.

The turbomachine engine of any preceding clause, wherein the redlinespeed is between seventy-five and one hundred seventy-five ft/sec.

The turbomachine engine of any preceding clause, wherein the redlinespeed is between one hundred fifty and two hundred fifty ft/sec.

The turbomachine engine of any preceding clause, wherein the ratio ofL_(MSR)/D_(MSR) is between twelve and twenty.

The turbomachine engine of any preceding clause, wherein the ratio ofL_(MSR)/D_(MSR) is between sixteen and thirty.

The turbomachine engine of any preceding clause, wherein the ratio ofL_(MSR)/D_(MSR) is between twenty-six and thirty-seven.

The turbomachine engine of any preceding clause, wherein the shaft is acomposite shaft made of at least two different materials.

The turbomachine engine of any preceding clause, wherein the shaft has alength L_(MSR) and a reduced mass density at a midpoint along the lengthL_(MSR).

The turbomachine engine of any preceding clause, wherein the shaft has areduced mass density at a midpoint along the length L_(MSR).

The turbomachine engine of any preceding clause, wherein the shaft is ahollow convex shaft with a reduced wall thickness at the midpoint, avariable inner diameter, and a constant outer diameter.

The turbomachine engine of any preceding clause, wherein the shaft is ahollow convex shaft with a reduced wall thickness at the midpoint, aconstant inner diameter, and a variable outer diameter.

The turbomachine engine of any preceding clause, wherein the shaft iscoupled to the power turbine at a first mounting point, and wherein theshaft is also coupled to one of the compressor sections at a secondmounting point.

The turbomachine engine of any preceding clause, wherein the shaft issupported by at least a first bearing and a second bearing.

The turbomachine engine of any preceding clause, wherein the shaft has alength L that is measured as the distance between the first bearing andthe second bearing.

The turbomachine engine of any preceding clause, wherein the length L ismeasured as the distance between the first bearing and the secondbearing.

The turbomachine engine of any preceding clause, wherein at least onebearing is a duplex bearing that has an overturning moment capability.

The turbomachine engine of any preceding clause, wherein each bearing isone of a ball bearing and a roller bearing.

The turbomachine engine of any preceding clause, wherein the firstbearing is positioned between the first mounting point and the secondmounting point, and wherein the second mounting point is positionedbetween the first bearing and the second bearing.

The turbomachine engine of any preceding clause, wherein the firstbearing and the second bearing support the shaft in an inboundconfiguration in which the first bearing and the second bearing arepositioned between the first mounting point and the second mountingpoint.

The turbomachine engine of any preceding clause, wherein the firstbearing and the second bearing support the shaft in an outboundconfiguration in which the first mounting point and the second mountingpoint are positioned between the first bearing and the second bearing.

The turbomachine engine of any preceding clause, wherein the shaft isfurther supported by a third bearing and a fourth bearing.

The turbomachine engine of any preceding clause, wherein the firstbearing and the second bearing are a first pair of duplex bearings, andthe third bearing and the fourth bearing are a second pair of duplexbearings, wherein the first pair of duplex bearings and the second pairof duplex bearings support the shaft in an inbound overturning momentconfiguration in which the first pair of duplex bearings and the secondpair of duplex bearings are positioned between the first mounting pointand the second mounting point.

The turbomachine engine of any preceding clause, wherein the firstbearing and the second bearing are a first pair of duplex bearings, andthe third bearing and the fourth bearing are a second pair of duplexbearings, wherein the first pair of duplex bearings and the second pairof duplex bearings support the shaft in an outbound overturning momentconfiguration in which the first mounting point and the second mountingpoint are positioned between the first pair of duplex bearings and thesecond pair of duplex bearings.

The turbomachine engine of any preceding clause, wherein the firstbearing, the second bearing, the third bearing, and the fourth bearingsupport the shaft in a four-bearing straddle configuration in which thefirst bearing and the second bearing are positioned between the firstmounting point and the second mounting point, and the first mountingpoint and the second mounting point are positioned between the thirdbearing and the fourth bearing.

The turbomachine engine of any preceding clause, wherein the firstbearing, the second bearing, the third bearing, and the fourth bearingsupport the shaft in a four-bearing outbound configuration in which thefirst mounting point and the second mounting point are positionedbetween a first group of bearings comprising the first bearing and thesecond bearing, and a second group of bearings comprising the thirdbearing and the fourth bearing.

In another aspect, a method includes using a turbomachine engine with acore having one or more compressor sections, one or more turbinesections that includes a power turbine, and a combustion chamber in flowcommunication with the compressor sections and turbine sections. Themethod also includes driving a shaft that is coupled to the powerturbine and that is characterized by a midshaft rating (MSR) between twohundred (ft/sec)^(1/2) and three hundred (ft/sec)^(1/2), and a redlinespeed between fifty and two hundred fifty feet per second (ft/sec).

In another aspect, a method includes using a turbomachine engine with acore having one or more compressor sections, one or more turbinesections that includes a power turbine, and a combustion chamber in flowcommunication with the compressor sections and turbine sections. Themethod also includes driving a shaft that is coupled to the powerturbine and that is characterized by a midshaft rating (MSR) between twohundred (ft/sec)^(1/2) and three hundred (ft/sec)^(1/2), a lengthL_(MSR), an outer diameter D_(MSR), and a ratio of L_(MSR)/D_(MSR)between twelve and thirty-seven.

The method of any preceding clause, wherein the turbomachine engine isconfigured to operate up to a redline speed without passing through acritical speed associated with a first-order bending mode of the shaft.

The method of any preceding clause, wherein the turbomachine engine isconfigured to operate up to the redline speed without passing through acritical speed associated with a first-order bending mode of the shaft.

The method of any preceding clause, wherein the MSR is between onehundred ninety (ft/sec)^(1/2) and two hundred forty-five (ft/sec)^(1/2).

The method of any preceding clause, wherein the MSR is between twohundred twelve (ft/sec)^(1/2) and two hundred sixty (ft/sec)^(1/2).

The method of any preceding clause, wherein the MSR is between twohundred forty-seven (ft/sec)^(1/2) and two hundred ninety(ft/sec)^(1/2).

The method of any preceding clause, wherein the redline speed is betweensixty and ninety ft/sec.

The method of any preceding clause, wherein the redline speed is betweenseventy-five and one hundred seventy-five ft/sec.

The method of any preceding clause, wherein the redline speed is betweenone hundred fifty and two hundred fifty ft/sec.

The method of any preceding clause, wherein the ratio of L_(MSR)/D_(MSR)is between twelve and twenty.

The method of any preceding clause, wherein the ratio of L_(MSR)/D_(MSR)is between sixteen and thirty.

The method of any preceding clause, wherein the ratio of L_(MSR)/D_(MSR)is between twenty-six and thirty-seven.

The method of any preceding clause, wherein the shaft is a compositeshaft made of at least two different materials.

The method of any preceding clause, wherein the shaft has a lengthL_(MSR) and a reduced mass density at a midpoint along the lengthL_(MSR).

The method of any preceding clause, wherein the shaft has a reduced massdensity at a midpoint along the length L.

The method of any preceding clause, wherein the shaft is a hollow convexshaft with a reduced wall thickness at the midpoint, a variable innerdiameter, and a constant outer diameter.

The method of any preceding clause, wherein the shaft is a hollow convexshaft with a reduced wall thickness at the midpoint, a constant innerdiameter, and a variable outer diameter.

The method of any preceding clause, wherein the shaft is coupled to thepower turbine at a first mounting point, and wherein the shaft is alsocoupled to one of the compressor sections at a second mounting point.

The method of any preceding clause, wherein the shaft is supported by atleast a first bearing and a second bearing.

The method of any preceding clause, wherein the shaft has a lengthL_(MSR) that is measured as the distance between the first bearing andthe second bearing.

The method of any preceding clause, wherein the length L_(MSR) ismeasured as the distance between the first bearing and the secondbearing.

The method of any preceding clause, wherein at least one bearing is aduplex bearing that has an overturning moment capability.

The method of any preceding clause, wherein each bearing is one of aball bearing and a roller bearing.

The method of any preceding clause, wherein the first bearing ispositioned between the first mounting point and the second mountingpoint, and wherein the second mounting point is positioned between thefirst bearing and the second bearing.

The method of any preceding clause, wherein the first bearing and thesecond bearing support the shaft in an inbound configuration in whichthe first bearing and the second bearing are positioned between thefirst mounting point and the second mounting point.

The method of any preceding clause, wherein the first bearing and thesecond bearing support the shaft in an outbound configuration in whichthe first mounting point and the second mounting point are positionedbetween the first bearing and the second bearing.

The method of any preceding clause, wherein the shaft is furthersupported by a third bearing and a fourth bearing.

The method of any preceding clause, wherein the first bearing and thesecond bearing are a first pair of duplex bearings, and the thirdbearing and the fourth bearing are a second pair of duplex bearings,wherein the first pair of duplex bearings and the second pair of duplexbearings support the shaft in an inbound overturning momentconfiguration in which the first pair of duplex bearings and the secondpair of duplex bearings are positioned between the first mounting pointand the second mounting point.

The method of any preceding clause, wherein the first bearing and thesecond bearing are a first pair of duplex bearings, and the thirdbearing and the fourth bearing are a second pair of duplex bearings,wherein the first pair of duplex bearings and the second pair of duplexbearings support the shaft in an outbound overturning momentconfiguration in which the first mounting point and the second mountingpoint are positioned between the first pair of duplex bearings and thesecond pair of duplex bearings.

The method of any preceding clause, wherein the first bearing, thesecond bearing, the third bearing, and the fourth bearing support theshaft in a four-bearing straddle configuration in which the firstbearing and the second bearing are positioned between the first mountingpoint and the second mounting point, and the first mounting point andthe second mounting point are positioned between the third bearing andthe fourth bearing.

The method of any preceding clause, wherein the first bearing, thesecond bearing, the third bearing, and the fourth bearing support theshaft in a four-bearing outbound configuration in which the firstmounting point and the second mounting point are positioned between afirst group of bearings including the first bearing and the secondbearing, and a second group of bearings including the third bearing andthe fourth bearing.

A turbomachine engine including a high-pressure compressor, ahigh-pressure turbine, a combustion chamber in flow communication withthe high-pressure compressor and the high-pressure turbine. Theturbomachine engine including a power turbine in flow communication withthe high-pressure turbine, wherein at least one of the high-pressurecompressor, the high-pressure turbine, or the power turbine includes aceramic matrix composite (CMC) material. The turbomachine engineincludes a low-pressure shaft coupled to the power turbine andcharacterized by a midshaft rating (MSR) between two hundred(ft/sec)^(1/2) and three hundred (ft/sec)^(1/2). The low-pressure shafthas a redline speed between fifty and two hundred fifty feet per second(ft/sec). The turbomachine engine is configured to operate up to theredline speed without passing through a critical speed associated with afirst-order bending mode of the low-pressure shaft.

A turbomachine engine includes a high-pressure compressor, ahigh-pressure turbine, a combustion chamber in flow communication withthe high-pressure compressor and the high-pressure turbine, a powerturbine in flow communication with the high-pressure turbine, wherein atleast one of the high-pressure compressor, the high-pressure turbine,and the power turbine including a ceramic matrix composite (CMC)material. The turbomachine engine includes a low-pressure shaft coupledto the power turbine. The low-pressure shaft configured to operate at alinear speed that does not exceed three hundred feet per second.

The turbomachine engine of any preceding clause, wherein the powerturbine includes the CMC material.

The turbomachine engine of any preceding clause, wherein the powerturbine includes at least one nozzle and at least one airfoil, whereinthe at least one nozzle, the at least one airfoil, or both the at leastone nozzle and the at least one airfoil include the CMC material.

The turbomachine engine of any preceding clause, wherein the powerturbine has three stages, four stages, five stages, or six stages, andwherein at least one stage includes the CMC material.

The turbomachine engine of any preceding clause, wherein the powerturbine has four stages and at least one stage of the four stagesincludes the CMC material.

The turbomachine engine of any preceding clause, wherein the CMCmaterial is a first CMC material, and wherein the high-pressure turbineincludes the first CMC material or a second CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor includes the first CMC material or the secondCMC material or a third CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine includes the CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine includes at least one nozzle and at least oneairfoil, wherein the at least one nozzle, the at least one airfoil, orboth the at least one nozzle and the at least one airfoil include theCMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine has one stage or two stages, and wherein at leastone stage includes the CMC material.

The turbomachine engine of any preceding clause, wherein the CMCmaterial is a first CMC material, and wherein the power turbine includesthe first CMC material or a second CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor includes the first CMC material or the secondCMC material or a third CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor includes the CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor has eight stages, nine stages, ten stages, oreleven stages, and wherein at least one stage includes the CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor has nine stages and at least one stage of thenine stages includes the CMC material.

The turbomachine engine of any preceding clause, wherein the CMCmaterial is a first CMC material, and wherein the high-pressure turbineincludes the first CMC material or a second CMC material.

The turbomachine engine of any preceding clause, wherein the powerturbine includes the first CMC material, the second CMC material, or athird CMC material.

The turbomachine engine of any preceding clause, wherein the first CMCmaterial and the second CMC material are the same materials.

The turbomachine engine of any preceding clause, wherein the first CMCmaterial and the second CMC material are different materials.

The turbomachine engine of any preceding clause, wherein the third CMCmaterial is the same material as the first CMC material, the second CMCmaterial, or both the first CMC material and the second CMC material.

The turbomachine engine of any preceding clause, wherein the third CMCmaterial is a different material than the first CMC material, the secondCMC material, or both the first CMC material and the second CMCmaterial.

The turbomachine engine of any preceding clause, further including anengine core including the high-pressure turbine, the high-pressurecompressor, and the combustion chamber, wherein the engine core has acore length (L_(CORE)) given by:

${L_{CORE} = {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}}},$where m is a number of stages of the high-pressure compressor, n is anumber of stages of the high-pressure turbine, and CIS is a constant.

The turbomachine engine of any preceding clause, further including ahigh-pressure shaft coupled between the high-pressure turbine and thehigh-pressure compressor and an engine core including the high-pressureturbine, the high-pressure compressor, and the combustion chamber,wherein the high-pressure shaft is characterized by a high-pressureshaft rating (HSR) given by:

${{HSR} = {10^{- 6}*N2_{r/l}*D_{CORE}*\left( \frac{L_{CORE}}{D_{CORE}} \right)^{2}}},$where N2_(r/l) is a redline speed of the high-pressure shaft, D_(CORE)is the diameter of an exit stage of the high-pressure compressor, andL_(CORE) is a core length of the engine core.

The turbomachine engine of any preceding clause, wherein thehigh-pressure shaft is characterized by a second high-pressure shaftrating (HSR_(LP)) given by:

${{HSR}_{LP} = {10^{- 6}*N1_{r/l}*D_{CORE}*\left( \frac{L_{CORE}}{D_{CORE}} \right)^{2}}},$where N1_(r/l) is the redline speed of the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine includes an airfoil configured with a forwardsurface facing towards a hot gas stream and a rearward surface facingaway from the hot gas stream, wherein the forward surface includes a CVItype CMC material and the rearward surface includes a MI type CMCmaterial.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine includes a CVI type CMC material and the powerturbine includes a MI type CMC material.

The turbomachine engine of any preceding clause, wherein the CMCmaterial includes a ceramic matrix material.

The turbomachine engine of any preceding clause, wherein the ceramicmatrix material includes a non-oxide silicon-based material.

The turbomachine engine of any preceding clause, wherein the non-oxidesilicon-based material is selected from the group consisting of siliconcarbide, silicon nitride, and mixtures thereof.

The turbomachine engine of any preceding clause, wherein the ceramicmatrix material includes an oxide ceramic material.

The turbomachine engine of any preceding clause, wherein the oxideceramic material is selected from the group consisting of siliconoxycarbides, silicon oxynitrides, aluminum oxide (Al₂O₃), silicondioxide (SiO₂), aluminosilicates, and mixtures thereof.

The turbomachine engine of any preceding clause, wherein the oxideceramic material includes oxides of element X, wherein X is selectedfrom the group consisting of silicon (Si), aluminum (Al), zirconium(Zr), yttrium (Y), and combinations thereof.

The turbomachine engine of any preceding clause, wherein the ceramicmatrix includes a non-oxide silicon-based material, an oxide ceramicmaterial, or mixtures thereof.

The turbomachine engine of any preceding clause, wherein the CMCmaterial includes a plurality of reinforcing fibers.

The turbomachine engine of any preceding clause, further including aflex coupling that couples the gearbox assembly to the low-speed shaft.

The turbomachine engine of any preceding clause, wherein the flexcoupling is characterized by a decoupler moment stiffness in a range of50 klb*in/rad to 200 klb*in/rad.

The turbomachine engine of any preceding clause, wherein the flexcoupling is characterized by a decoupler shear stiffness in a range of100 klb/in to 500 klb/in.

The turbomachine engine of any preceding clause, the decoupler momentstiffness being equal to

$\frac{E*K_{m}*R_{dcplr}^{4}}{H_{dcplr}},$E being a Young's modulus of a material of the flex coupling, K_(m)being a correction factor, R_(dcplr) being a decoupler radius of theflex coupling, and H_(dcplr) being a decoupler height of the flexcoupling.

The turbomachine engine of any preceding clause, K_(m) being in a rangeof 0.13×10⁻³ to 0.27×10⁻³.

The turbomachine engine of any preceding clause, the decoupler shearstiffness being equal to

$\frac{E*K_{m}*R_{dcplr}^{4}}{L_{dcplr}^{2}},$wherein E being a Young's modulus of a material of the flex coupling,K_(m) being a correction factor, R_(dcplr) being a decoupler radius ofthe flex coupling, and L_(dcplr) being a decoupler length of the flexcoupling.

The turbomachine engine of any preceding clause, K_(m) being in a rangeof 0.13×10⁻³ to 0.27×10⁻³.

The turbomachine engine of any preceding clause, wherein the MSR isbetween one hundred ninety (ft/sec)^(1/2) and two hundred forty-five(ft/sec)^(1/2).

The turbomachine engine of any preceding clause, wherein the MSR isbetween two hundred twelve (ft/sec)^(1/2) and two hundred sixty(ft/sec)^(1/2).

The turbomachine engine of any preceding clause, wherein the MSR isbetween two hundred forty-seven (ft/sec)^(1/2) and two hundred ninety(ft/sec)^(1/2).

The turbomachine engine of any preceding clause, wherein HSR is from 1.9to 4.3.

The turbomachine engine of any preceding clause, wherein D_(CORE) isfrom 13 inches to 41 inches.

The turbomachine engine of any preceding clause, wherein L_(CORE) isfrom 43 inches to 80 inches.

The turbomachine engine of any preceding clause, wherein N2_(r/l) isfrom 11000 RPM to 25000 RPM.

The turbomachine engine of any preceding clause, wherein m is eight,nine, ten, or eleven.

The turbomachine engine of any preceding clause, wherein n is one ortwo.

The turbomachine engine of any preceding clause, wherein CIS is fromtwenty inches to thirty inches.

The turbomachine engine of any preceding clause, wherein HSR_(LP) isfrom 1.1 to 1.6.

The turbomachine engine of any preceding clause, wherein thehigh-pressure shaft first mode margin with respect to the low-pressureshaft redline speed is given by:

${0 < {\frac{0.55}{\left( {HSR}_{LP} \right)^{2}} + {LST}} < {- 0.2}},$wherein LST accounts for the effects that the HPC pressure ratio and theHPC exit temperature can have on the first mode.

The turbomachine engine of any preceding clause, wherein LST is from−0.2 to −0.74.

The turbomachine engine of any preceding clause, wherein thehigh-pressure shaft second mode margin with respect to the high-pressureshaft redline speed is given by:

${{{{- 0.1215}*{HSR}} + \left( \frac{{2*{HST}} - 1}{3} \right)} < {- 0.2}},$wherein HST accounts for the effects that the HPC pressure ratio and theHPC exit temperature have on the third mode.

The turbomachine engine of any preceding clause, wherein HST is from0.46 to 0.78.

The turbomachine engine of any preceding clause, wherein thelow-pressure shaft has a length (L_(MSR)) that extends from a forwardbearing to an aft bearing, and a mid-shaft diameter (D_(MSR)), andwherein the length (L_(MSR)) is given by:L_(MSR)=L_(IGB)+L_(CORE)+L_(AFT), where L_(IGB) is a length forward ofthe core engine to the forward bearing, L_(CORE) is a length of the coreengine, and L_(AFT) is a length from aft of the core engine to the aftbearing.

The turbomachine engine of any preceding clause, wherein L_(MSR) isgiven by:

${L_{MSR} = {\left\lbrack {{0.16*D_{CORE}} + 1.7} \right\rbrack + \left\lbrack {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}} \right\rbrack + L_{AFT}}},$where m is a number of stages of the high-pressure compressor, n is anumber of stages of the high-pressure turbine, and CIS is a constant.

The turbomachine engine of any preceding clause, wherein L_(IGB) is fromfour inches to twelve inches.

The turbomachine engine of any preceding clause, wherein L_(AFT) is fromtwo inches to twenty-four inches.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor includes an exit stage having an exit stagediameter (D_(CORE)).

The turbomachine engine of any preceding clause, wherein L_(IGB) isgiven by: L_(IGB)=0.16*D_(CORE)+1.7

The turbomachine engine of any preceding clause, wherein D_(MSR) isgiven by: D_(MSR)=D_(HPT BORE)−2*t, where D_(HPT BORE) is a diameter ofa bore of the high-pressure turbine and t is an intershaft thicknessbetween the shaft and the bore of the high-pressure turbine.

The turbomachine engine of any preceding clause, wherein the thicknessis from 450 mils to 650 mils.

The turbomachine engine of any preceding clause, further including acore forward bearing and a core aft bearing.

The turbomachine engine of any preceding clause, wherein the lengthL_(IGB) extends from the forward bearing to the core forward bearing.

The turbomachine engine of any preceding clause, wherein the lengthL_(AFT) extends from the aft bearing to the core aft bearing.

The turbomachine engine of any preceding clause, wherein the lengthL_(CORE) extends from the core forward bearing to the core aft bearing.

The turbomachine engine of any preceding clause, wherein the engine isan unducted engine.

The turbomachine engine of any preceding clause, wherein the engine is aducted engine.

The turbomachine engine of any preceding clause, further including asecond aft bearing.

The turbomachine engine of any preceding clause, further including asecond forward bearing and a second aft bearing.

The turbomachine engine of any preceding clause, wherein the forwardbearing is forward of the high-pressure compressor.

The turbomachine engine of any preceding clause, wherein the aft bearingis aft of the high-pressure turbine.

The turbomachine engine of any preceding clause, wherein thelow-pressure turbine has five stages and at least one stage of the fivestages includes the CMC material.

The turbomachine engine of any preceding clause, wherein thelow-pressure turbine has six stages and at least one stage of the sixstages includes the CMC material.

The turbomachine engine of any preceding clause, wherein thelow-pressure turbine has three stages and at least one stage of thethree stages includes the CMC material.

The turbomachine engine of any preceding clause, wherein thelow-pressure turbine and the high-pressure compressor each include a CMCmaterial.

The turbomachine engine of any preceding clause, wherein thelow-pressure turbine and the high-pressure turbine each include a CMCmaterial.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor and the high-pressure turbine each include aCMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine has one stage, and wherein the stage includes theCMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine has two stages, and wherein at least one stage ofthe two stages includes the CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor has eight stages and at least one stage of theeight stages includes the CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor has ten stages and at least one stage of theten stages includes the CMC material.

The turbomachine engine of any preceding clause, wherein thehigh-pressure compressor has eleven stages and at least one stage of theeleven stages includes the CMC material.

The turbomachine engine of any preceding clause, wherein the engine isan open fan engine having a first second and third stream, and wherein aratio of a primary fan to a mid-fan blade spans is between 2:1 to 10:1.

The turbomachine engine of any preceding clause, wherein the engine isan open fan engine having a first second and third stream, and wherein aratio of a primary fan to a mid-fan blade spans is between 3:1 to 7:1.

The turbomachine engine of any preceding clause, wherein the engine isan open fan or ducted engine.

The turbomachine engine of any preceding clause, wherein the linearspeed of the low-pressure shaft is greater than thirty feet per second.

The turbomachine engine of any preceding clause, wherein the ceramicmatrix includes an inorganic filler.

The turbomachine engine of any preceding clause, wherein the inorganicfiller is selected from the group consisting of pyrophyllite,wollastonite, mica, talc, kyanite, montmorillonite, and mixturesthereof.

The turbomachine engine of any preceding clause, wherein the ceramicmatrix includes a non-oxide silicon-based material, an oxide ceramicmaterial, or mixtures thereof.

The turbomachine engine of any preceding clause, wherein the CMCmaterial includes a plurality of reinforcing fibers.

The turbomachine engine of any preceding clause, wherein the pluralityof reinforcing fibers includes a non-oxide silicon-based material.

The turbomachine engine of any preceding clause, wherein the non-oxidesilicon-based material is selected from the group consisting of siliconcarbide, silicon nitride, and mixtures thereof.

The turbomachine engine of any preceding clause, wherein the pluralityof reinforcing fibers includes an oxide ceramic material.

The turbomachine engine of any preceding clause, wherein the oxideceramic is selected from the group consisting of silicon oxycarbides,silicon oxynitrides, aluminum oxide (Al2O3), silicon dioxide (SiO2),aluminosilicates, and mixtures thereof.

The turbomachine engine of any preceding clause, the plurality ofreinforcing fibers includes a non-oxide carbon-based material.

The turbomachine engine of any preceding clause, wherein the ceramicmatrix includes a non-oxide silicon-based material, an oxide ceramicmaterial, a non-oxide carbon-based material, or mixtures thereof.

The turbomachine engine of any preceding clause, further including anelectric machine coupled to the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein the electricmachine is located aft of the power turbine.

The turbomachine engine of any preceding clause, wherein the electricmachine is an electric motor.

The turbomachine engine of any preceding clause, wherein the electricmachine is an electric generator.

The turbomachine engine of any preceding clause, wherein the electricmachine includes a rotor and a stator, wherein the rotor rotates withrespect to the stator.

The turbomachine engine of any preceding clause, wherein the rotor iscoupled to the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein the rotor isconfigured to rotate with the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein the electricmachine is a motor-generator.

A method of operating the turbomachine engine of any preceding clause,the method including operating the turbomachine engine to generate anengine thrust wherein a linear speed of the low-pressure shaft does notexceed three hundred feet per second.

A method of operating a turbomachine engine having a high-pressurecompressor, a high-pressure turbine, a combustion chamber in flowcommunication with the high-pressure compressor and the high-pressureturbine, a power turbine, at least one of the high-pressure compressor,the high-pressure turbine, and the power turbine having a ceramic matriccomposite (CMC) material, and a low-pressure shaft coupled to the powerturbine and characterized by a midshaft rating (MSR) between two hundred(ft/sec)^(1/2) and three hundred (ft/sec)^(1/2). The method includingoperating the low-pressure shaft up to the redline speed between fiftyand two hundred fifty feet per second (ft/sec) without passing through acritical speed associated with a first-order bending mode of thelow-pressure shaft.

A method of operating a turbomachine engine having a high-pressurecompressor, a high-pressure turbine, a combustion chamber in flowcommunication with the high-pressure compressor and the high-pressureturbine, a power turbine in flow communication with the high-pressureturbine, at least one of the high-pressure compressor, the high-pressureturbine, or the power turbine having a ceramic matrix composite (CMC)material, and a low-pressure shaft coupled to the power turbine. Themethod including operating the low-pressure shaft at a linear speed thatdoes not exceed three hundred feet per second.

The method of any preceding clause, wherein the turbomachine engine isthe turbomachine engine according to any preceding clause.

A turbomachine engine including an engine core including a high-pressurecompressor, which has an exit stage having an exit stage diameter(D_(CORE)), a high-pressure turbine, and a combustion chamber in flowcommunication with the high-pressure compressor and the high-pressureturbine; a power turbine in flow communication with the high-pressureturbine; and a low-pressure shaft coupled to the power turbine andcharacterized by a midshaft rating (MSR) between two hundred(ft/sec)^(1/2) and three hundred (ft/sec)^(1/2). The low-pressure shafthas a redline speed between fifty and two hundred fifty feet per second(ft/sec). The turbomachine engine is configured to operate up to theredline speed without passing through a critical speed associated with afirst-order bending mode of the low-pressure shaft. The low-pressureshaft has a length (L_(MSR)) defined by an engine core length (L_(CORE))given by:

${L_{CORE} = {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}}},$where m is a number of stages of the high-pressure compressor, n is anumber of stages of the high-pressure turbine, and CIS is a constant.

A turbomachine engine having an engine core including a high-pressurecompressor, which has an exit stage having an exit stage diameter(D_(CORE)), having from eight stages to eleven stages, a high-pressureturbine, and a combustion chamber in flow communication with thehigh-pressure compressor and the high-pressure turbine, wherein the highpressure compressor and higher pressure turbine are connected through ahigh pressure shaft; and wherein the high-pressure compressor andhigh-pressure turbine are related to a core length (L_(CORE)) by

${L_{CORE} = {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}}},$where m is a number of stages of the high-pressure compressor, n is anumber of stages of the high-pressure turbine, and CIS is a constant.The turbomachine engine further comprising a power turbine in flowcommunication with the high-pressure turbine and a low-pressure shaftcoupling the power turbine to a low-pressure compressor and fanassembly, wherein the low-pressure shaft has a redline speed of between50 feet per second and 300 feet per second.

The turbomachine engine of any preceding clause, wherein CIS is fromtwenty inches to thirty inches.

The turbomachine engine of any preceding clause, wherein L_(CORE) isfrom forty-three inches to eighty inches.

The turbomachine engine of any preceding clause, wherein D_(CORE) isfrom 13 inches to 41 inches.

The turbomachine engine of any preceding clause, wherein the powerturbine has four stages, five stages, or six stages.

The turbomachine engine of any preceding clause, wherein n is one stageor two stages.

The turbomachine engine of any preceding clause, wherein m is eightstages, nine stages, ten stages, or eleven stages.

The turbomachine engine of any preceding clause, wherein m is ninestages.

The turbomachine engine of any preceding clause, wherein thehigh-pressure turbine and the high-pressure compressor are connected toeach other through a high-pressure shaft, and wherein the high-pressureshaft is characterized by a high-pressure shaft rating (HSR) given by:

${{HSR} = {10^{- 6}*N\; 2_{r/l}*D_{CORE}*\left( \frac{L_{CORE}}{D_{CORE}} \right)^{2}}},$where N2_(r/l) is a redline speed of the high-pressure shaft.

The turbomachine engine of any preceding clause, wherein HSR is from 1.9to 4.3.

The turbomachine engine of any preceding clause, wherein N2_(r/l) isfrom 11000 RPM to 25000 RPM.

The turbomachine engine of any preceding clause, wherein thehigh-pressure shaft is characterized by a second high-pressure shaftrating (HSRLP) given by:

${{HSR}_{LP} = {10^{- 6}*N\; 1_{r/l}*D_{CORE}*\left( \frac{L_{CORE}}{D_{CORE}} \right)^{2}}},$where N1_(r/l) is the redline speed of the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein HSR_(LP) isfrom 1.1 to 1.6.

The turbomachine engine of any preceding clause, wherein the powerturbine comprises a ceramic matrix composite (CMC) material.

The turbomachine engine of any preceding clause, further including anelectric machine coupled to the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein the electricmachine is located aft of the power turbine.

The turbomachine engine of any preceding clause, further comprising aprimary fan driven by the power turbine through a gearbox assembly and aflex coupling that couples the gearbox assembly to the low-pressureshaft.

The turbomachine engine of any preceding clause, wherein the flexcoupling is characterized by a decoupler moment stiffness in a range of50 klb*in/rad to 200 klb*in/rad and a decoupler shear stiffness in arange of 100 klb/in to 500 klb/in.

The turbomachine engine of any preceding clause, wherein the length(L_(MSR)) is given by: L_(MSR)=L_(IGB)+L_(CORE)+L_(AFT), where L_(IGB)is a length forward of the core engine to the forward bearing and isfrom four inches to twelve inches and L_(AFT) is a length from aft ofthe core engine to the aft bearing and is from two inches to twenty-fourinches.

The turbomachine engine of any preceding clause, wherein the electricmachine is an electric motor.

The turbomachine engine of any preceding clause, wherein the electricmachine is an electric generator.

The turbomachine engine of any preceding clause, wherein the electricmachine includes a rotor and a stator, wherein the rotor rotates withrespect to the stator.

The turbomachine engine of any preceding clause, wherein the rotor iscoupled to the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein the rotor isconfigured to rotate with the low-pressure shaft.

The turbomachine engine of any preceding clause, wherein the electricmachine is a motor-generator.

The method of any preceding clause, wherein the engine is an open fan orducted engine.

The turbomachine engine of any preceding clause, wherein the flexcoupling is characterized by a decoupler moment stiffness in a range of50 klb*in/rad to 200 klb*in/rad.

The turbomachine engine of any preceding clause, wherein the flexcoupling is characterized by a decoupler shear stiffness in a range of100 klb/in to 500 klb/in.

The turbomachine engine of any preceding clause, the decoupler momentstiffness being equal to

$\frac{E*K_{m}*R_{dcplr}^{4}}{H_{dcplr}},$E being a Young's modulus of a material of the flex coupling, K_(m)being a correction factor, R_(dcplr) being a decoupler radius of theflex coupling, and H_(dcplr) being a decoupler height of the flexcoupling.

The turbomachine engine of any preceding clause, K_(m) being in a rangeof 0.13×10⁻³ to 0.27×10⁻³.

The turbomachine engine of any preceding clause, the decoupler shearstiffness being equal to

$\frac{E*K_{m}*R_{dcplr}^{4}}{L_{dcplr}^{2}},$wherein E being a Young's modulus of a material of the flex coupling,K_(m) being a correction factor, R_(dcplr) being a decoupler radius ofthe flex coupling, and L_(dcplr) being a decoupler length of the flexcoupling.

The turbomachine engine of any preceding clause, K_(m) being in a rangeof 0.13×10⁻³ to 0.27×10⁻³.

The turbomachine of any preceding clause, wherein the MSR is between onehundred ninety (ft/sec)½ and two hundred forty-five (ft/sec)½.

The turbomachine of any preceding clause, wherein the MSR is between twohundred twelve (ft/sec)½ and two hundred sixty (ft/sec)½.

The turbomachine of any preceding clause, wherein the MSR is between twohundred forty-seven (ft/sec)½ and two hundred ninety (ft/sec)½.

The turbomachine engine of any preceding clause, wherein thehigh-pressure shaft first mode margin with respect to the low-pressureshaft redline speed is given by:

${0 < {\frac{0.55}{\left( {HSR}_{LP} \right)^{2}} + {LST}} < {- 0.2}},$wherein LST accounts for the effects that the HPC pressure ratio and theHPC exit temperature can have on the first mode.

The turbomachine engine of any preceding clause, wherein LST is from−0.2 to −0.74.

The turbomachine engine of any preceding clause, wherein thehigh-pressure shaft second mode margin with respect to the high-pressureshaft redline speed is given by:

${{{{- 0.1215}*{HSR}} + \left( \frac{{2*{HST}} - 1}{3} \right)} < {- 0.2}},$wherein HST accounts for the effects that the HPC pressure ratio and theHPC exit temperature have on the third mode.

The turbomachine engine of any preceding clause, wherein HST is from0.46 to 0.78.

The turbomachine engine of any preceding clause, wherein the engine isan open fan engine having a first second and third stream, and wherein aratio of a primary fan to a mid-fan blade spans is between 2:1 to 10:1.

The turbomachine engine of any preceding clause, wherein the engine isan open fan engine having a first second and third stream, and wherein aratio of a primary fan to a mid-fan blade spans is between 3:1 to 7:1.

The turbomachine of any preceding clause, wherein L_(IGB) is from fourinches to twelve inches.

The turbomachine of any preceding clause, wherein L_(AFT) is between twoinches and twenty-four inches, inclusive of the endpoints.

The turbomachine of any preceding clause, wherein L_(IGB) is given byL_(IGB)=0.16*D_(CORE)+1.7.

The turbomachine of any preceding clause, wherein D_(MSR) is given by:D_(MSR)=D_(HPT BORE)−2*t, where D_(HPT BORE) is a diameter of a bore ofthe high-pressure turbine and t is an intershaft thickness between theshaft and the bore of the high-pressure turbine.

The turbomachine of any preceding clause, wherein the thickness isbetween 450 mils and 650 mils, inclusive of the endpoints.

The turbomachine of any preceding clause, wherein at least one of thepower turbine, the high-pressure compressor, and the high-pressureturbine comprises a ceramic matrix composite (CMC).

The turbomachine engine of any preceding clause, further comprising acore forward bearing and a core aft bearing.

The turbomachine engine of any preceding clause, wherein the lengthL_(IGB) extends from the forward bearing to the core forward bearing.

The turbomachine engine of any preceding clause, wherein the lengthL_(AFT) extends from the aft bearing to the core aft bearing.

The turbomachine engine of any preceding clause, wherein the lengthL_(CORE) extends from the core forward bearing to the core aft bearing.

The turbomachine engine of any preceding clause, wherein the engine isan unducted engine.

The turbomachine engine of any preceding clause, wherein the engine is aducted engine.

The turbomachine engine of any preceding clause, further comprising asecond aft bearing.

The turbomachine engine of any preceding clause, further comprising asecond forward bearing.

The turbomachine engine of any preceding clause, wherein the forwardbearing is forward of the high-pressure compressor.

The turbomachine engine of any preceding clause, wherein the aft bearingis aft of the high-pressure turbine.

A method of operating the turbomachine engine of any preceding clause,the method including operating the turbomachine engine to generate anengine thrust wherein a linear speed of the low-pressure shaft does notexceed three hundred feet per second.

A method of operating a turbomachine engine including an engine coreincluding a high-pressure compressor, which has an exit stage having anexit stage diameter (D_(CORE)), a high-pressure turbine, a combustionchamber in flow communication with the high-pressure compressor and thehigh-pressure turbine, a power turbine in flow communication with thehigh-pressure turbine, and a low-pressure shaft coupled to the powerturbine and characterized by a midshaft rating (MSR) between two hundred(ft/sec)^(1/2) and three hundred (ft/sec)^(1/2) and having a length(L_(MSR)) defined by an engine core length (L_(CORE)) given by:

${L_{CORE} = {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}}},$where m is a number of stages of the high-pressure compressor, n is anumber of stages of the high-pressure turbine, and CIS is a constant.The method including operating the low-pressure shaft at a redline speedbetween fifty and two hundred fifty feet per second (ft/sec). The methodincluding operating the low-pressure shaft up to the redline speedwithout passing through a critical speed associated with a first-orderbending mode of the low-pressure shaft.

A method of operating a turbomachine, comprising the steps of: using anengine core including a high-pressure compressor, which has an exitstage having an exit stage diameter (D_(CORE)), a high-pressure turbine,and a combustion chamber in flow communication with the high-pressurecompressor and the high-pressure turbine, a power turbine in flowcommunication with the high-pressure turbine, and a low-pressure shaftcoupled to the power turbine and characterized by a midshaft rating(MSR) between two hundred (ft/sec)^(1/2) and three hundred(ft/sec)^(1/2). The method includes operating the turbomachine togenerate an engine thrust wherein the low-pressure shaft linear speeddoes not exceed three hundred feet per second.

A method of operating a turbomachine engine, comprising using an enginecore including a high-pressure compressor, which has an exit stagehaving an exit stage diameter (D_(CORE)), a high-pressure turbine, acombustion chamber in flow communication with the high-pressurecompressor and the high-pressure turbine, a power turbine in flowcommunication with the high-pressure turbine, and a low-pressure shaftcoupled to the power turbine having a length (L_(MSR)) defined by anengine core length (L_(CORE)) given by:

${L_{CORE} = {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}}},$where m is a number of stages of the high-pressure compressor, n is anumber of stages of the high-pressure turbine, and CIS is a constant.The method including operating the turbomachine engine to generate anengine thrust wherein a linear speed of the low-pressure shaft does notexceed three hundred feet per second.

The method of any preceding clause, wherein the turbomachine engine isthe turbomachine engine according to any preceding clause.

Although the foregoing description is directed to certain embodiments,other variations and modifications will be apparent to those skilled inthe art, and may be made without departing from the scope of thedisclosure. Moreover, features described in connection with oneembodiment may be used in conjunction with other embodiments, even ifnot explicitly stated above.

The invention claimed is:
 1. A turbomachine engine comprising: ahigh-pressure compressor; a high-pressure turbine; a combustion chamberin flow communication with the high-pressure compressor and thehigh-pressure turbine; a power turbine in flow communication with thehigh-pressure turbine, wherein at least one of the high-pressurecompressor, the high-pressure turbine, and the power turbine comprises aceramic matrix composite (CMC) material; and a low-pressure shaftcoupled to the power turbine and characterized by a midshaft rating(MSR) between two hundred (ft/sec)^(1/2) and three hundred(ft/sec)^(1/2), wherein the low-pressure shaft has a redline speedbetween fifty and two hundred fifty feet per second (ft/sec), andwherein the turbomachine engine is configured to operate up to theredline speed without passing through a critical speed associated with afirst-order bending mode of the low-pressure shaft.
 2. The turbomachineengine of claim 1, further comprising an engine core comprising thehigh-pressure turbine, the high-pressure compressor, and the combustionchamber, wherein the engine core has a core length (L_(CORE)) given by:${L_{CORE} = {{\left\lbrack {m^{({20 + m})}*n^{({10 + n})}} \right\rbrack^{(\frac{1}{100})}*D_{CORE}} + {CIS}}},$where m is a number of stages of the high-pressure compressor, n is anumber of stages of the high-pressure turbine, and CIS is a constant. 3.The turbomachine engine of claim 1, further comprising a high-pressureshaft coupled between the high-pressure turbine and the high-pressurecompressor and an engine core comprising the high-pressure turbine, thehigh-pressure compressor, and the combustion chamber, wherein thehigh-pressure shaft is characterized by a high-pressure shaft rating(HSR_(LP)) given by:${{HSR}_{LP} = {10^{- 6}*N\; 1_{r/l}*D_{CORE}*\left( \frac{L_{CORE}}{D_{CORE}} \right)^{2}}},$where N1_(r/l) is a redline speed of the low-pressure shaft, D_(CORE) isa diameter of an exit stage of the high-pressure compressor, andL_(CORE) is a core length of the engine core.
 4. The turbomachine engineof claim 1, further including an electric machine coupled to thelow-pressure shaft.
 5. The turbomachine engine of claim 1, wherein thehigh-pressure turbine comprises an airfoil configured with a forwardsurface facing towards a hot gas stream and a rearward surface facingaway from the hot gas stream, wherein the forward surface and therearward surface each comprise the CMC material, and wherein the CMCmaterial in the forward surface comprises a CVI type CMC material andthe CMC material in the rearward surface comprises a MI type CMCmaterial.
 6. The turbomachine engine of claim 1, wherein thehigh-pressure turbine comprises a CVI type CMC material and the powerturbine comprises a MI type CMC material.
 7. The turbomachine engine ofclaim 1, wherein the CMC material includes a plurality of reinforcingfibers.
 8. The turbomachine engine of claim 1, wherein the power turbinecomprises the CMC material.
 9. The turbomachine engine of claim 8,wherein the power turbine comprises at least one nozzle and at least oneairfoil, wherein the at least one nozzle, the at least one airfoil, orboth the at least one nozzle and the at least one airfoil comprise theCMC material.
 10. The turbomachine engine of claim 8, wherein the powerturbine has three stages, four stages, five stages, or six stages, andwherein at least one stage of the three stages, the four stages, thefive stages, or the six stages comprises the CMC material.
 11. Theturbomachine engine of claim 8, wherein the power turbine has fourstages and at least one stage of the four stages comprises the CMCmaterial.
 12. The turbomachine engine of claim 8, wherein the CMCmaterial is a first CMC material, and wherein the high-pressure turbinecomprises the first CMC material or a second CMC material.
 13. Theturbomachine engine of claim 12, wherein the high-pressure compressorcomprises the first CMC material or the second CMC material or a thirdCMC material.
 14. The turbomachine engine of claim 1, wherein thehigh-pressure turbine comprises the CMC material.
 15. The turbomachineengine of claim 14, wherein the high-pressure turbine comprises at leastone nozzle and at least one airfoil, wherein the at least one nozzle,the at least one airfoil, or both the at least one nozzle and the atleast one airfoil comprise the CMC material.
 16. The turbomachine engineof claim 14, wherein the high-pressure turbine has one stage or twostages, and wherein the one stage or at least one stage of the twostages comprises the CMC material.
 17. The turbomachine engine of claim1, wherein the high-pressure compressor comprises the CMC material. 18.The turbomachine engine of claim 17, wherein the high-pressurecompressor has eight stages, nine stages, ten stages, or eleven stages,and wherein at least one stage of the eight stages, nine stages, tenstages, or eleven stages comprises the CMC material.
 19. Theturbomachine engine of claim 17, wherein the high-pressure compressorhas nine stages and at least one stage of the nine stages comprises theCMC material.
 20. The turbomachine engine of claim 17, wherein the CMCmaterial is a first CMC material, and wherein the high-pressure turbinecomprises the first CMC material or a second CMC material.
 21. Theturbomachine engine of claim 1, wherein the CMC material includes aceramic matrix material comprising a non-oxide silicon-based material,an oxide ceramic material, or mixtures thereof.
 22. The turbomachineengine of claim 21, wherein the ceramic matrix material is SiC and theCMC material is reinforced with a plurality of SiC or C fibers.
 23. Theturbomachine engine of claim 21, wherein the ceramic matrix materialincludes the non-oxide silicon-based material.
 24. The turbomachineengine of claim 23, wherein the non-oxide silicon-based material isselected from the group consisting of silicon carbide, silicon nitride,and mixtures thereof.
 25. The turbomachine engine of claim 21, whereinthe ceramic matrix material includes the oxide ceramic material.
 26. Theturbomachine engine of claim 25, wherein the oxide ceramic material isselected from the group consisting of silicon oxycarbides, siliconoxynitrides, aluminum oxide (Al₂O₃), silicon dioxide (SiO₂),aluminosilicates, and mixtures thereof.
 27. The turbomachine engine ofclaim 25, wherein the oxide ceramic material includes oxides of elementX, wherein X is selected from the group consisting of silicon (Si),aluminum (Al), zirconium (Zr), yttrium (Y), and combinations thereof.